TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Orive, Ramon
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3157
AB  - Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization of the well-known Micchelli-Rivlin quadrature formula. The others are new. A numerically stable construction of these quadratures is proposed. By determining the absolute value of the difference between these Gaussian quadratures with multiple nodes for the Fourier-Chebyshev coefficients and their corresponding optimal extensions, we get the well-known methods for estimating their error. Numerical results are included. These results are a continuation of the recent ones in Bojanov & Petrova (2009, J. Comput. Appl. Math., 231, 378-391) and Milovanovic & Spalevic (2014, Math. Comput., 83, 1207-1231).
PB  - Oxford Univ Press, Oxford
T2  - Ima Journal of Numerical Analysis
T1  - Quadratures with multiple nodes for Fourier-Chebyshev coefficients
EP  - 296
IS  - 1
SP  - 271
VL  - 39
DO  - 10.1093/imanum/drx067
ER  - 

@article{
author = "Milovanović, Gradimir V. and Orive, Ramon and Spalević, Miodrag",
year = "2019",
abstract = "Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization of the well-known Micchelli-Rivlin quadrature formula. The others are new. A numerically stable construction of these quadratures is proposed. By determining the absolute value of the difference between these Gaussian quadratures with multiple nodes for the Fourier-Chebyshev coefficients and their corresponding optimal extensions, we get the well-known methods for estimating their error. Numerical results are included. These results are a continuation of the recent ones in Bojanov & Petrova (2009, J. Comput. Appl. Math., 231, 378-391) and Milovanovic & Spalevic (2014, Math. Comput., 83, 1207-1231).",
publisher = "Oxford Univ Press, Oxford",
journal = "Ima Journal of Numerical Analysis",
title = "Quadratures with multiple nodes for Fourier-Chebyshev coefficients",
pages = "296-271",
number = "1",
volume = "39",
doi = "10.1093/imanum/drx067"
}

Milovanović, G. V., Orive, R.,& Spalević, M.. (2019). Quadratures with multiple nodes for Fourier-Chebyshev coefficients. in Ima Journal of Numerical Analysis
Oxford Univ Press, Oxford., 39(1), 271-296.
https://doi.org/10.1093/imanum/drx067

Milovanović GV, Orive R, Spalević M. Quadratures with multiple nodes for Fourier-Chebyshev coefficients. in Ima Journal of Numerical Analysis. 2019;39(1):271-296.
doi:10.1093/imanum/drx067 .

Milovanović, Gradimir V., Orive, Ramon, Spalević, Miodrag, "Quadratures with multiple nodes for Fourier-Chebyshev coefficients" in Ima Journal of Numerical Analysis, 39, no. 1 (2019):271-296,
https://doi.org/10.1093/imanum/drx067 . .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Pranić, Miroslav S.
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3083
AB  - The paper deals with new contributions to the theory of the Gauss quadrature formulas with multiple nodes that are published after 2001, including numerical construction, error analysis and applications. The first part was published in Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellan, and L. Reichel, eds.) [J. Comput. Appl. Math. 127 (2001), no. 1-2, 267-286].
PB  - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2  - Applicable Analysis and Discrete Mathematics
T1  - Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii
EP  - 27
IS  - 1
SP  - 1
VL  - 13
DO  - 10.2298/AADM180730018M
ER  - 

@article{
author = "Milovanović, Gradimir V. and Pranić, Miroslav S. and Spalević, Miodrag",
year = "2019",
abstract = "The paper deals with new contributions to the theory of the Gauss quadrature formulas with multiple nodes that are published after 2001, including numerical construction, error analysis and applications. The first part was published in Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials (W. Gautschi, F. Marcellan, and L. Reichel, eds.) [J. Comput. Appl. Math. 127 (2001), no. 1-2, 267-286].",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii",
pages = "27-1",
number = "1",
volume = "13",
doi = "10.2298/AADM180730018M"
}

Milovanović, G. V., Pranić, M. S.,& Spalević, M.. (2019). Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(1), 1-27.
https://doi.org/10.2298/AADM180730018M

Milovanović GV, Pranić MS, Spalević M. Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii. in Applicable Analysis and Discrete Mathematics. 2019;13(1):1-27.
doi:10.2298/AADM180730018M .

Milovanović, Gradimir V., Pranić, Miroslav S., Spalević, Miodrag, "Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part ii" in Applicable Analysis and Discrete Mathematics, 13, no. 1 (2019):1-27,
https://doi.org/10.2298/AADM180730018M . .

TY  - JOUR
AU  - Cvetković, Aleksandar
AU  - Milovanović, Gradimir V.
AU  - Vasović, Nevena
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2940
AB  - Given real number s > -1/2 and the second degree monic Chebyshev polynomial of the first kind (T) over cap (2)(x), we consider the polynomial system {p(k)(2,s)} "induced" by the modified measure d sigma(2,s) (x) = vertical bar(T) over cap (2)(x)vertical bar(2s) d sigma(x) = 1/root 1 - x(2) dx is the Chebyshev measure of the first kind. We determine the coefficients of the three-term recurrence relation for the polynomials p(k)(2,s) (x) in an analytic form and derive a differential equality, as well as the differential equation for these orthogonal polynomials. Assuming a logarithmic potential, we also give an electrostatic interpretation of the zeros of p(4 nu)(2,s) (x)(nu is an element of N).
PB  - SPRINGER Basel AG, Basel
T2  - Results in Mathematics
T1  - Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials
IS  - 1
VL  - 73
DO  - 10.1007/s00025-018-0779-8
ER  - 

@article{
author = "Cvetković, Aleksandar and Milovanović, Gradimir V. and Vasović, Nevena",
year = "2018",
abstract = "Given real number s > -1/2 and the second degree monic Chebyshev polynomial of the first kind (T) over cap (2)(x), we consider the polynomial system {p(k)(2,s)} "induced" by the modified measure d sigma(2,s) (x) = vertical bar(T) over cap (2)(x)vertical bar(2s) d sigma(x) = 1/root 1 - x(2) dx is the Chebyshev measure of the first kind. We determine the coefficients of the three-term recurrence relation for the polynomials p(k)(2,s) (x) in an analytic form and derive a differential equality, as well as the differential equation for these orthogonal polynomials. Assuming a logarithmic potential, we also give an electrostatic interpretation of the zeros of p(4 nu)(2,s) (x)(nu is an element of N).",
publisher = "SPRINGER Basel AG, Basel",
journal = "Results in Mathematics",
title = "Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials",
number = "1",
volume = "73",
doi = "10.1007/s00025-018-0779-8"
}

Cvetković, A., Milovanović, G. V.,& Vasović, N.. (2018). Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials. in Results in Mathematics
SPRINGER Basel AG, Basel., 73(1).
https://doi.org/10.1007/s00025-018-0779-8

Cvetković A, Milovanović GV, Vasović N. Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials. in Results in Mathematics. 2018;73(1).
doi:10.1007/s00025-018-0779-8 .

Cvetković, Aleksandar, Milovanović, Gradimir V., Vasović, Nevena, "Recurrence Relation and Differential Equation for a Class of Orthogonal Polynomials" in Results in Mathematics, 73, no. 1 (2018),
https://doi.org/10.1007/s00025-018-0779-8 . .

TY  - JOUR
AU  - Spalević, Miodrag
AU  - Cvetković, Aleksandar
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2448
AB  - The estimation of the error in a quadrature formula is an important problem. A simple and effective procedure for estimating the error of Gaussian quadrature formulas using their extensions with multiple nodes will be presented. Our method works for estimating the error of any interpolatory quadrature formula with simple or multiple nodes. We concentrate the most of our attention to the estimation of the error of standard Gauss quadratures, as the most known and popular ones. In that sense we offer an adequate alternative to Gauss-Kronrod quadratures, which have been intensively investigated in the last five decades, both from the theoretical and computational point of view. We found and a few cases of optimal, i.e., Kronrod extensions with multiple nodes for some Gauss quadrature formulas; we are not aware of any results of this kind in the mathematical literature. Numerical results are presented, in order to demonstrate the efficiency of the proposed method.
PB  - Springer, Dordrecht
T2  - Bit Numerical Mathematics
T1  - Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes
EP  - 374
IS  - 1
SP  - 357
VL  - 56
DO  - 10.1007/s10543-015-0551-3
ER  - 

@article{
author = "Spalević, Miodrag and Cvetković, Aleksandar",
year = "2016",
abstract = "The estimation of the error in a quadrature formula is an important problem. A simple and effective procedure for estimating the error of Gaussian quadrature formulas using their extensions with multiple nodes will be presented. Our method works for estimating the error of any interpolatory quadrature formula with simple or multiple nodes. We concentrate the most of our attention to the estimation of the error of standard Gauss quadratures, as the most known and popular ones. In that sense we offer an adequate alternative to Gauss-Kronrod quadratures, which have been intensively investigated in the last five decades, both from the theoretical and computational point of view. We found and a few cases of optimal, i.e., Kronrod extensions with multiple nodes for some Gauss quadrature formulas; we are not aware of any results of this kind in the mathematical literature. Numerical results are presented, in order to demonstrate the efficiency of the proposed method.",
publisher = "Springer, Dordrecht",
journal = "Bit Numerical Mathematics",
title = "Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes",
pages = "374-357",
number = "1",
volume = "56",
doi = "10.1007/s10543-015-0551-3"
}

Spalević, M.,& Cvetković, A.. (2016). Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes. in Bit Numerical Mathematics
Springer, Dordrecht., 56(1), 357-374.
https://doi.org/10.1007/s10543-015-0551-3

Spalević M, Cvetković A. Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes. in Bit Numerical Mathematics. 2016;56(1):357-374.
doi:10.1007/s10543-015-0551-3 .

Spalević, Miodrag, Cvetković, Aleksandar, "Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes" in Bit Numerical Mathematics, 56, no. 1 (2016):357-374,
https://doi.org/10.1007/s10543-015-0551-3 . .

TY  - JOUR
AU  - Cvetković, Aleksandar
AU  - Spalević, Miodrag
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1965
AB  - We consider extensions of Kronrod-type and extensions obtained by generalized averaged Gaussian quadrature formulas for Gauss-Turan quadrature formulas. Existence and uniqueness of these extensions are considered. Their numerical construction is proposed. It is the first general method and is based on a combination of well-known numerical methods for Gauss-Turan, Gauss, Gauss-Kronrod, Anti-Gauss, and generalized averaged Gaussian quadratures. We employ these extensions for estimating the remainder terms in the Gauss-Turan quadratures. Numerical results are presented.
PB  - Kent State University
T2  - Electronic Transactions on Numerical Analysis
T1  - Estimating the error of gauss-turan quadrature formulas using their extensions
EP  - 12
SP  - 1
VL  - 41
UR  - https://hdl.handle.net/21.15107/rcub_machinery_1965
ER  - 

@article{
author = "Cvetković, Aleksandar and Spalević, Miodrag",
year = "2014",
abstract = "We consider extensions of Kronrod-type and extensions obtained by generalized averaged Gaussian quadrature formulas for Gauss-Turan quadrature formulas. Existence and uniqueness of these extensions are considered. Their numerical construction is proposed. It is the first general method and is based on a combination of well-known numerical methods for Gauss-Turan, Gauss, Gauss-Kronrod, Anti-Gauss, and generalized averaged Gaussian quadratures. We employ these extensions for estimating the remainder terms in the Gauss-Turan quadratures. Numerical results are presented.",
publisher = "Kent State University",
journal = "Electronic Transactions on Numerical Analysis",
title = "Estimating the error of gauss-turan quadrature formulas using their extensions",
pages = "12-1",
volume = "41",
url = "https://hdl.handle.net/21.15107/rcub_machinery_1965"
}

Cvetković, A.,& Spalević, M.. (2014). Estimating the error of gauss-turan quadrature formulas using their extensions. in Electronic Transactions on Numerical Analysis
Kent State University., 41, 1-12.
https://hdl.handle.net/21.15107/rcub_machinery_1965

Cvetković A, Spalević M. Estimating the error of gauss-turan quadrature formulas using their extensions. in Electronic Transactions on Numerical Analysis. 2014;41:1-12.
https://hdl.handle.net/21.15107/rcub_machinery_1965 .

Cvetković, Aleksandar, Spalević, Miodrag, "Estimating the error of gauss-turan quadrature formulas using their extensions" in Electronic Transactions on Numerical Analysis, 41 (2014):1-12,
https://hdl.handle.net/21.15107/rcub_machinery_1965 .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Spalević, Miodrag
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1951
AB  - We continue with analyzing quadrature formulas of high degree of precision for computing the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials, started recently by Bojanov and Petrova [Quadrature formulae for Fourier coefficients, J. Comput. Appl. Math. 231 (2009), 378-391] and we extend their results. Construction of new Gaussian quadrature formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives, is considered. We prove the existence and uniqueness of Kronrod extensions with multiple nodes of standard Gaussian quadrature formulas with multiple nodes for several weight functions, in order to construct some new generalizations of quadrature formulas for the Fourier coefficients. For the quadrature formulas for the Fourier coefficients based on the zeros of the corresponding orthogonal polynomials we construct Kronrod extensions with multiple nodes and highest algebraic degree of precision. For this very desirable kind of extension there do not exist any results in the theory of standard quadrature formulas.
T2  - Mathematics of Computation
T1  - Kronrod extensions with multiple nodes of quadrature formulas for fourier coefficients
EP  - 1231
IS  - 287
SP  - 1207
VL  - 83
DO  - 10.1090/S0025-5718-2013-02761-5
ER  - 

@article{
author = "Milovanović, Gradimir V. and Spalević, Miodrag",
year = "2014",
abstract = "We continue with analyzing quadrature formulas of high degree of precision for computing the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials, started recently by Bojanov and Petrova [Quadrature formulae for Fourier coefficients, J. Comput. Appl. Math. 231 (2009), 378-391] and we extend their results. Construction of new Gaussian quadrature formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives, is considered. We prove the existence and uniqueness of Kronrod extensions with multiple nodes of standard Gaussian quadrature formulas with multiple nodes for several weight functions, in order to construct some new generalizations of quadrature formulas for the Fourier coefficients. For the quadrature formulas for the Fourier coefficients based on the zeros of the corresponding orthogonal polynomials we construct Kronrod extensions with multiple nodes and highest algebraic degree of precision. For this very desirable kind of extension there do not exist any results in the theory of standard quadrature formulas.",
journal = "Mathematics of Computation",
title = "Kronrod extensions with multiple nodes of quadrature formulas for fourier coefficients",
pages = "1231-1207",
number = "287",
volume = "83",
doi = "10.1090/S0025-5718-2013-02761-5"
}

Milovanović, G. V.,& Spalević, M.. (2014). Kronrod extensions with multiple nodes of quadrature formulas for fourier coefficients. in Mathematics of Computation, 83(287), 1207-1231.
https://doi.org/10.1090/S0025-5718-2013-02761-5

Milovanović GV, Spalević M. Kronrod extensions with multiple nodes of quadrature formulas for fourier coefficients. in Mathematics of Computation. 2014;83(287):1207-1231.
doi:10.1090/S0025-5718-2013-02761-5 .

Milovanović, Gradimir V., Spalević, Miodrag, "Kronrod extensions with multiple nodes of quadrature formulas for fourier coefficients" in Mathematics of Computation, 83, no. 287 (2014):1207-1231,
https://doi.org/10.1090/S0025-5718-2013-02761-5 . .

TY  - JOUR
AU  - Stanić, Marija P.
AU  - Cvetković, Aleksandar
AU  - Tomović, Tatjana V.
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1850
AB  - In this paper, we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on (-,) for integrand analytic in a certain domain of complex plane.
PB  - Wiley-Blackwell, Hoboken
T2  - Mathematical Methods in The Applied Sciences
T1  - Error estimates for some quadrature rules with maximal trigonometric degree of exactness
EP  - 1699
IS  - 11
SP  - 1687
VL  - 37
DO  - 10.1002/mma.2929
ER  - 

@article{
author = "Stanić, Marija P. and Cvetković, Aleksandar and Tomović, Tatjana V.",
year = "2014",
abstract = "In this paper, we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on (-,) for integrand analytic in a certain domain of complex plane.",
publisher = "Wiley-Blackwell, Hoboken",
journal = "Mathematical Methods in The Applied Sciences",
title = "Error estimates for some quadrature rules with maximal trigonometric degree of exactness",
pages = "1699-1687",
number = "11",
volume = "37",
doi = "10.1002/mma.2929"
}

Stanić, M. P., Cvetković, A.,& Tomović, T. V.. (2014). Error estimates for some quadrature rules with maximal trigonometric degree of exactness. in Mathematical Methods in The Applied Sciences
Wiley-Blackwell, Hoboken., 37(11), 1687-1699.
https://doi.org/10.1002/mma.2929

Stanić MP, Cvetković A, Tomović TV. Error estimates for some quadrature rules with maximal trigonometric degree of exactness. in Mathematical Methods in The Applied Sciences. 2014;37(11):1687-1699.
doi:10.1002/mma.2929 .

Stanić, Marija P., Cvetković, Aleksandar, Tomović, Tatjana V., "Error estimates for some quadrature rules with maximal trigonometric degree of exactness" in Mathematical Methods in The Applied Sciences, 37, no. 11 (2014):1687-1699,
https://doi.org/10.1002/mma.2929 . .

TY  - JOUR
AU  - Stanić, Marija P.
AU  - Cvetković, Aleksandar
AU  - Tomović, Tatjana V.
PY  - 2014
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1879
AB  - In this paper an error estimate for quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes) for periodic integrand, analytic in a circular domain, is given. Theoretical estimate is illustrated by numerical example.
PB  - Springer-Verlag Italia Srl, Milan
T2  - Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas
T1  - Error estimates for quadrature rules with maximal even trigonometric degree of exactness
EP  - 615
IS  - 2
SP  - 603
VL  - 108
DO  - 10.1007/s13398-013-0129-3
ER  - 

@article{
author = "Stanić, Marija P. and Cvetković, Aleksandar and Tomović, Tatjana V.",
year = "2014",
abstract = "In this paper an error estimate for quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes) for periodic integrand, analytic in a circular domain, is given. Theoretical estimate is illustrated by numerical example.",
publisher = "Springer-Verlag Italia Srl, Milan",
journal = "Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas",
title = "Error estimates for quadrature rules with maximal even trigonometric degree of exactness",
pages = "615-603",
number = "2",
volume = "108",
doi = "10.1007/s13398-013-0129-3"
}

Stanić, M. P., Cvetković, A.,& Tomović, T. V.. (2014). Error estimates for quadrature rules with maximal even trigonometric degree of exactness. in Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas
Springer-Verlag Italia Srl, Milan., 108(2), 603-615.
https://doi.org/10.1007/s13398-013-0129-3

Stanić MP, Cvetković A, Tomović TV. Error estimates for quadrature rules with maximal even trigonometric degree of exactness. in Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas. 2014;108(2):603-615.
doi:10.1007/s13398-013-0129-3 .

Stanić, Marija P., Cvetković, Aleksandar, Tomović, Tatjana V., "Error estimates for quadrature rules with maximal even trigonometric degree of exactness" in Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas, 108, no. 2 (2014):603-615,
https://doi.org/10.1007/s13398-013-0129-3 . .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Pejčev, Aleksandar
AU  - Spalević, Miodrag
PY  - 2013
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1662
AB  - In two BIT papers error expansions in the Gauss and Gauss-Turan quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s є N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s є N0) has been supposed in one of the mentioned papers. Here, we prove that formula.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight
EP  - 1042
IS  - 6
SP  - 1037
VL  - 27
DO  - 10.2298/FIL1306037M
ER  - 

@article{
author = "Milovanović, Gradimir V. and Pejčev, Aleksandar and Spalević, Miodrag",
year = "2013",
abstract = "In two BIT papers error expansions in the Gauss and Gauss-Turan quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s є N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s є N0) has been supposed in one of the mentioned papers. Here, we prove that formula.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight",
pages = "1042-1037",
number = "6",
volume = "27",
doi = "10.2298/FIL1306037M"
}

Milovanović, G. V., Pejčev, A.,& Spalević, M.. (2013). A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 27(6), 1037-1042.
https://doi.org/10.2298/FIL1306037M

Milovanović GV, Pejčev A, Spalević M. A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight. in Filomat. 2013;27(6):1037-1042.
doi:10.2298/FIL1306037M .

Milovanović, Gradimir V., Pejčev, Aleksandar, Spalević, Miodrag, "A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight" in Filomat, 27, no. 6 (2013):1037-1042,
https://doi.org/10.2298/FIL1306037M . .

TY  - JOUR
AU  - Cirić, Vladimir
AU  - Cvetković, Aleksandar
AU  - Simić, Vladimir
AU  - Milentijević, Ivan
PY  - 2013
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1707
AB  - Nanotechnology is yet to come, but even now, in early stage of development it is clear that defect and fault levels will be much higher than current CMOS technology. The exact level of defect densities is unknown, but it is assumed that 1-15% on-chip resources will be defective. Novel techniques and architectures have to be devised in order for nanoelectronics to become a viable replacement for current VLSI processes. With defect rates for current VLSI processes in the range of 1 part per billion, manufacturers can afford to discard any chip that is found to be defective. However, in order to increase fabrication yield, nanotechnology requires extensive and computationally demanding analysis of defect significance. In order to simplify the analysis, in this paper we propose a mathematical framework based on tropical algebra for circuit analysis. It is more descriptive and convenient to use in graph analysis than traditional algebra. In tropical algebra, we will derive a simple iterative algorithm for error propagation analysis of systolic arrays. It will be shown that the computational complexity of the proposed algorithm is reduced from O(T-3) to O(T-2), where T is the number of array cells. An example of tropical algebra analysis and design of partially defect tolerant hexagonal systolic multiplier will be given, too.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - Tropical algebra based framework for error propagation analysis in systolic arrays
EP  - 525
SP  - 512
VL  - 225
DO  - 10.1016/j.amc.2013.09.059
ER  - 

@article{
author = "Cirić, Vladimir and Cvetković, Aleksandar and Simić, Vladimir and Milentijević, Ivan",
year = "2013",
abstract = "Nanotechnology is yet to come, but even now, in early stage of development it is clear that defect and fault levels will be much higher than current CMOS technology. The exact level of defect densities is unknown, but it is assumed that 1-15% on-chip resources will be defective. Novel techniques and architectures have to be devised in order for nanoelectronics to become a viable replacement for current VLSI processes. With defect rates for current VLSI processes in the range of 1 part per billion, manufacturers can afford to discard any chip that is found to be defective. However, in order to increase fabrication yield, nanotechnology requires extensive and computationally demanding analysis of defect significance. In order to simplify the analysis, in this paper we propose a mathematical framework based on tropical algebra for circuit analysis. It is more descriptive and convenient to use in graph analysis than traditional algebra. In tropical algebra, we will derive a simple iterative algorithm for error propagation analysis of systolic arrays. It will be shown that the computational complexity of the proposed algorithm is reduced from O(T-3) to O(T-2), where T is the number of array cells. An example of tropical algebra analysis and design of partially defect tolerant hexagonal systolic multiplier will be given, too.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "Tropical algebra based framework for error propagation analysis in systolic arrays",
pages = "525-512",
volume = "225",
doi = "10.1016/j.amc.2013.09.059"
}

Cirić, V., Cvetković, A., Simić, V.,& Milentijević, I.. (2013). Tropical algebra based framework for error propagation analysis in systolic arrays. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 225, 512-525.
https://doi.org/10.1016/j.amc.2013.09.059

Cirić V, Cvetković A, Simić V, Milentijević I. Tropical algebra based framework for error propagation analysis in systolic arrays. in Applied Mathematics and Computation. 2013;225:512-525.
doi:10.1016/j.amc.2013.09.059 .

Cirić, Vladimir, Cvetković, Aleksandar, Simić, Vladimir, Milentijević, Ivan, "Tropical algebra based framework for error propagation analysis in systolic arrays" in Applied Mathematics and Computation, 225 (2013):512-525,
https://doi.org/10.1016/j.amc.2013.09.059 . .

TY  - CONF
AU  - Stanić, Marija P.
AU  - Cvetković, Aleksandar
AU  - Tomović, Tatjana V.
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1345
AB  - In this paper we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on (-pi, pi) for integrand analytic in certain domain of complex plane.
PB  - Amer Inst Physics, Melville
C3  - Numerical Analysis and Applied Mathematics (Icnaam 2012), Vols A and B
T1  - Error Bounds for Some Quadrature Rules With Maximal Trigonometric Degree of Exactness
EP  - 1045
SP  - 1042
VL  - 1479
DO  - 10.1063/1.4756324
ER  - 

@conference{
author = "Stanić, Marija P. and Cvetković, Aleksandar and Tomović, Tatjana V.",
year = "2012",
abstract = "In this paper we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on (-pi, pi) for integrand analytic in certain domain of complex plane.",
publisher = "Amer Inst Physics, Melville",
journal = "Numerical Analysis and Applied Mathematics (Icnaam 2012), Vols A and B",
title = "Error Bounds for Some Quadrature Rules With Maximal Trigonometric Degree of Exactness",
pages = "1045-1042",
volume = "1479",
doi = "10.1063/1.4756324"
}

Stanić, M. P., Cvetković, A.,& Tomović, T. V.. (2012). Error Bounds for Some Quadrature Rules With Maximal Trigonometric Degree of Exactness. in Numerical Analysis and Applied Mathematics (Icnaam 2012), Vols A and B
Amer Inst Physics, Melville., 1479, 1042-1045.
https://doi.org/10.1063/1.4756324

Stanić MP, Cvetković A, Tomović TV. Error Bounds for Some Quadrature Rules With Maximal Trigonometric Degree of Exactness. in Numerical Analysis and Applied Mathematics (Icnaam 2012), Vols A and B. 2012;1479:1042-1045.
doi:10.1063/1.4756324 .

Stanić, Marija P., Cvetković, Aleksandar, Tomović, Tatjana V., "Error Bounds for Some Quadrature Rules With Maximal Trigonometric Degree of Exactness" in Numerical Analysis and Applied Mathematics (Icnaam 2012), Vols A and B, 1479 (2012):1042-1045,
https://doi.org/10.1063/1.4756324 . .

TY  - JOUR
AU  - Stanić, Marija P.
AU  - Cvetković, Aleksandar
AU  - Tomović, Tatjana V.
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1484
AB  - In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function w(x) = 1+cos x, x ∈ (−π, π), for 2π -periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.
PB  - Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac
T2  - Kragujevac Journal of Mathematics
T1  - Error bound of certain Gaussian quadrature rules for trigonometric polynomials
EP  - 72
IS  - 1
SP  - 63
VL  - 36
UR  - https://hdl.handle.net/21.15107/rcub_machinery_1484
ER  - 

@article{
author = "Stanić, Marija P. and Cvetković, Aleksandar and Tomović, Tatjana V.",
year = "2012",
abstract = "In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function w(x) = 1+cos x, x ∈ (−π, π), for 2π -periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.",
publisher = "Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac",
journal = "Kragujevac Journal of Mathematics",
title = "Error bound of certain Gaussian quadrature rules for trigonometric polynomials",
pages = "72-63",
number = "1",
volume = "36",
url = "https://hdl.handle.net/21.15107/rcub_machinery_1484"
}

Stanić, M. P., Cvetković, A.,& Tomović, T. V.. (2012). Error bound of certain Gaussian quadrature rules for trigonometric polynomials. in Kragujevac Journal of Mathematics
Univerzitet u Kragujevcu - Prirodno-matematički fakultet, Kragujevac., 36(1), 63-72.
https://hdl.handle.net/21.15107/rcub_machinery_1484

Stanić MP, Cvetković A, Tomović TV. Error bound of certain Gaussian quadrature rules for trigonometric polynomials. in Kragujevac Journal of Mathematics. 2012;36(1):63-72.
https://hdl.handle.net/21.15107/rcub_machinery_1484 .

Stanić, Marija P., Cvetković, Aleksandar, Tomović, Tatjana V., "Error bound of certain Gaussian quadrature rules for trigonometric polynomials" in Kragujevac Journal of Mathematics, 36, no. 1 (2012):63-72,
https://hdl.handle.net/21.15107/rcub_machinery_1484 .

TY  - JOUR
AU  - Cvetković, Aleksandar
AU  - Milovanović, Gradimir V.
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1411
AB  - Interval quadrature formulae of Gaussian type on R and R+ for exponential weight functions of the form w(x) = exp(-Q(x)), where Q is a continuous function on its domain and such that all algebraic polynomials are integrable with respect to w, are considered. For a given set of nonoverlapping intervals and an arbitrary n, the uniqueness of the n-point interval Gaussian rule is proved. The results can be applied also to corresponding quadratures over (-1, 1). An algorithm for the numerical construction of interval quadratures is presented. Finally, in order to illustrate the presented method, two numerical examples are done.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - Gaussian interval quadrature rule for exponential weights
EP  - 9341
IS  - 18
SP  - 9332
VL  - 218
DO  - 10.1016/j.amc.2012.03.016
ER  - 

@article{
author = "Cvetković, Aleksandar and Milovanović, Gradimir V.",
year = "2012",
abstract = "Interval quadrature formulae of Gaussian type on R and R+ for exponential weight functions of the form w(x) = exp(-Q(x)), where Q is a continuous function on its domain and such that all algebraic polynomials are integrable with respect to w, are considered. For a given set of nonoverlapping intervals and an arbitrary n, the uniqueness of the n-point interval Gaussian rule is proved. The results can be applied also to corresponding quadratures over (-1, 1). An algorithm for the numerical construction of interval quadratures is presented. Finally, in order to illustrate the presented method, two numerical examples are done.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "Gaussian interval quadrature rule for exponential weights",
pages = "9341-9332",
number = "18",
volume = "218",
doi = "10.1016/j.amc.2012.03.016"
}

Cvetković, A.,& Milovanović, G. V.. (2012). Gaussian interval quadrature rule for exponential weights. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 218(18), 9332-9341.
https://doi.org/10.1016/j.amc.2012.03.016

Cvetković A, Milovanović GV. Gaussian interval quadrature rule for exponential weights. in Applied Mathematics and Computation. 2012;218(18):9332-9341.
doi:10.1016/j.amc.2012.03.016 .

Cvetković, Aleksandar, Milovanović, Gradimir V., "Gaussian interval quadrature rule for exponential weights" in Applied Mathematics and Computation, 218, no. 18 (2012):9332-9341,
https://doi.org/10.1016/j.amc.2012.03.016 . .

TY  - JOUR
AU  - Cvetković, Aleksandar
AU  - Stanić, Marija P.
AU  - Marjanović, Zvezdan M.
AU  - Tomović, Tatjana V.
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1500
AB  - Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x) on (0, 2 pi) have been considered firstly by Turetzkii [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337-359 (translation in English from Uchenye Zapiski, Vypusk 1(149), Seria Math. Theory of Functions, Collection of papers, Izdatel'stvo Belgosuniversiteta imeni V.I. Lenina, Minsk, (1959) pp. 31-54)]. Such orthogonal systems are connected with quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes), which have application in numerical integration of 2 pi-periodic functions. In this paper we study asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree with respect to a strictly positive weight function satisfying the Lipschitz-Dini condition.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree
EP  - 11533
IS  - 23
SP  - 11528
VL  - 218
DO  - 10.1016/j.amc.2012.04.082
ER  - 

@article{
author = "Cvetković, Aleksandar and Stanić, Marija P. and Marjanović, Zvezdan M. and Tomović, Tatjana V.",
year = "2012",
abstract = "Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x) on (0, 2 pi) have been considered firstly by Turetzkii [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337-359 (translation in English from Uchenye Zapiski, Vypusk 1(149), Seria Math. Theory of Functions, Collection of papers, Izdatel'stvo Belgosuniversiteta imeni V.I. Lenina, Minsk, (1959) pp. 31-54)]. Such orthogonal systems are connected with quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes), which have application in numerical integration of 2 pi-periodic functions. In this paper we study asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree with respect to a strictly positive weight function satisfying the Lipschitz-Dini condition.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree",
pages = "11533-11528",
number = "23",
volume = "218",
doi = "10.1016/j.amc.2012.04.082"
}

Cvetković, A., Stanić, M. P., Marjanović, Z. M.,& Tomović, T. V.. (2012). Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 218(23), 11528-11533.
https://doi.org/10.1016/j.amc.2012.04.082

Cvetković A, Stanić MP, Marjanović ZM, Tomović TV. Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree. in Applied Mathematics and Computation. 2012;218(23):11528-11533.
doi:10.1016/j.amc.2012.04.082 .

Cvetković, Aleksandar, Stanić, Marija P., Marjanović, Zvezdan M., Tomović, Tatjana V., "Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree" in Applied Mathematics and Computation, 218, no. 23 (2012):11528-11533,
https://doi.org/10.1016/j.amc.2012.04.082 . .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Cvetković, Aleksandar
AU  - Stanić, Marija P.
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1472
AB  - In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semi- integer degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.
PB  - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
T2  - Filomat
T1  - A trigonometric orthogonality with respect to a nonnegative Borel measure
EP  - 696
IS  - 4
SP  - 689
VL  - 26
DO  - 10.2298/FIL1204689M
ER  - 

@article{
author = "Milovanović, Gradimir V. and Cvetković, Aleksandar and Stanić, Marija P.",
year = "2012",
abstract = "In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semi- integer degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.",
publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš",
journal = "Filomat",
title = "A trigonometric orthogonality with respect to a nonnegative Borel measure",
pages = "696-689",
number = "4",
volume = "26",
doi = "10.2298/FIL1204689M"
}

Milovanović, G. V., Cvetković, A.,& Stanić, M. P.. (2012). A trigonometric orthogonality with respect to a nonnegative Borel measure. in Filomat
Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 26(4), 689-696.
https://doi.org/10.2298/FIL1204689M

Milovanović GV, Cvetković A, Stanić MP. A trigonometric orthogonality with respect to a nonnegative Borel measure. in Filomat. 2012;26(4):689-696.
doi:10.2298/FIL1204689M .

Milovanović, Gradimir V., Cvetković, Aleksandar, Stanić, Marija P., "A trigonometric orthogonality with respect to a nonnegative Borel measure" in Filomat, 26, no. 4 (2012):689-696,
https://doi.org/10.2298/FIL1204689M . .

TY  - JOUR
AU  - Stanić, Marija P.
AU  - Cvetković, Aleksandar
AU  - Simić, Suzana
AU  - Dimitrijević, Sladjana
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1389
AB  - The purpose of this article is to generalize common fixed point theorems under contractive condition of A dagger iriA double dagger's type on a cone metric type space. We give basic facts about cone metric type spaces, and we prove common fixed point theorems under contractive condition of A dagger iriA double dagger's type on a cone metric type space without assumption of normality for cone. As special cases we get the corresponding fixed point theorems on a cone metric space with respect to a solid cone. Obtained results in this article extend, generalize, and improve, well-known comparable results in the literature. 2000 Mathematics Subject Classification: 47H10; 54H25; 55M20.
PB  - Springer International Publishing Ag, Cham
T2  - Fixed Point Theory and Applications
T1  - Common fixed point under contractive condition of Ciric's type on cone metric type spaces
DO  - 10.1186/1687-1812-2012-35
ER  - 

@article{
author = "Stanić, Marija P. and Cvetković, Aleksandar and Simić, Suzana and Dimitrijević, Sladjana",
year = "2012",
abstract = "The purpose of this article is to generalize common fixed point theorems under contractive condition of A dagger iriA double dagger's type on a cone metric type space. We give basic facts about cone metric type spaces, and we prove common fixed point theorems under contractive condition of A dagger iriA double dagger's type on a cone metric type space without assumption of normality for cone. As special cases we get the corresponding fixed point theorems on a cone metric space with respect to a solid cone. Obtained results in this article extend, generalize, and improve, well-known comparable results in the literature. 2000 Mathematics Subject Classification: 47H10; 54H25; 55M20.",
publisher = "Springer International Publishing Ag, Cham",
journal = "Fixed Point Theory and Applications",
title = "Common fixed point under contractive condition of Ciric's type on cone metric type spaces",
doi = "10.1186/1687-1812-2012-35"
}

Stanić, M. P., Cvetković, A., Simić, S.,& Dimitrijević, S.. (2012). Common fixed point under contractive condition of Ciric's type on cone metric type spaces. in Fixed Point Theory and Applications
Springer International Publishing Ag, Cham..
https://doi.org/10.1186/1687-1812-2012-35

Stanić MP, Cvetković A, Simić S, Dimitrijević S. Common fixed point under contractive condition of Ciric's type on cone metric type spaces. in Fixed Point Theory and Applications. 2012;.
doi:10.1186/1687-1812-2012-35 .

Stanić, Marija P., Cvetković, Aleksandar, Simić, Suzana, Dimitrijević, Sladjana, "Common fixed point under contractive condition of Ciric's type on cone metric type spaces" in Fixed Point Theory and Applications (2012),
https://doi.org/10.1186/1687-1812-2012-35 . .

TY  - JOUR
AU  - Pavlović, V.
AU  - Cvetković, Aleksandar
PY  - 2012
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1575
AB  - Given a mapping f : X -> X, we naturally associate to it a monotonic map gamma(f) : exp X -> exp X from the power set of X into itself, and thus inducing a generalized topology on X. Here, we investigate some properties of generalized topologies as defined by such a procedure.
T2  - Bulletin of the Iranian Mathematical Society
T1  - On generalized topologies arising from mappings
EP  - 565
IS  - 3
SP  - 553
VL  - 38
UR  - https://hdl.handle.net/21.15107/rcub_machinery_1575
ER  - 

@article{
author = "Pavlović, V. and Cvetković, Aleksandar",
year = "2012",
abstract = "Given a mapping f : X -> X, we naturally associate to it a monotonic map gamma(f) : exp X -> exp X from the power set of X into itself, and thus inducing a generalized topology on X. Here, we investigate some properties of generalized topologies as defined by such a procedure.",
journal = "Bulletin of the Iranian Mathematical Society",
title = "On generalized topologies arising from mappings",
pages = "565-553",
number = "3",
volume = "38",
url = "https://hdl.handle.net/21.15107/rcub_machinery_1575"
}

Pavlović, V.,& Cvetković, A.. (2012). On generalized topologies arising from mappings. in Bulletin of the Iranian Mathematical Society, 38(3), 553-565.
https://hdl.handle.net/21.15107/rcub_machinery_1575

Pavlović V, Cvetković A. On generalized topologies arising from mappings. in Bulletin of the Iranian Mathematical Society. 2012;38(3):553-565.
https://hdl.handle.net/21.15107/rcub_machinery_1575 .

Pavlović, V., Cvetković, Aleksandar, "On generalized topologies arising from mappings" in Bulletin of the Iranian Mathematical Society, 38, no. 3 (2012):553-565,
https://hdl.handle.net/21.15107/rcub_machinery_1575 .

TY  - JOUR
AU  - Cvetković, Aleksandar
AU  - Stanić, Marija P.
AU  - Dimitrijević, Sladjana
AU  - Simić, Suzana
PY  - 2011
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1147
AB  - In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. We prove some common fixed point theorems for four mappings in those spaces. Obtained results extend and generalize well-known comparable results in the literature. All results are proved in the settings of a solid cone, without the assumption of continuity of mappings.
PB  - Springer International Publishing Ag, Cham
T2  - Fixed Point Theory and Applications
T1  - Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space
DO  - 10.1155/2011/589725
ER  - 

@article{
author = "Cvetković, Aleksandar and Stanić, Marija P. and Dimitrijević, Sladjana and Simić, Suzana",
year = "2011",
abstract = "In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. We prove some common fixed point theorems for four mappings in those spaces. Obtained results extend and generalize well-known comparable results in the literature. All results are proved in the settings of a solid cone, without the assumption of continuity of mappings.",
publisher = "Springer International Publishing Ag, Cham",
journal = "Fixed Point Theory and Applications",
title = "Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space",
doi = "10.1155/2011/589725"
}

Cvetković, A., Stanić, M. P., Dimitrijević, S.,& Simić, S.. (2011). Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space. in Fixed Point Theory and Applications
Springer International Publishing Ag, Cham..
https://doi.org/10.1155/2011/589725

Cvetković A, Stanić MP, Dimitrijević S, Simić S. Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space. in Fixed Point Theory and Applications. 2011;.
doi:10.1155/2011/589725 .

Cvetković, Aleksandar, Stanić, Marija P., Dimitrijević, Sladjana, Simić, Suzana, "Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space" in Fixed Point Theory and Applications (2011),
https://doi.org/10.1155/2011/589725 . .

TY  - JOUR
AU  - Stanić, Marija P.
AU  - Cvetković, Aleksandar
PY  - 2011
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1141
AB  - In this paper we consider polynomials orthogonal with respect to the linear functional L : P -> C, defined on the space of all algebraic polynomials P by L[p] = integral(1)(-1)p(x)(1 - x)(alpha-1/2)(1 + x)(beta-1/2)exp(i zeta x)dx, where alpha, beta > 1/2 are real numbers such that l = vertical bar beta - alpha vertical bar is a positive integer, and zeta is an element of R\{0}. We prove the existence of such orthogonal polynomials for some pairs of alpha and zeta and for all nonnegative integers l. For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference relations. For such orthogonal polynomials the corresponding quadrature rules of Gaussian type are considered. Also, some numerical examples are included.
PB  - Global Science Press
T2  - Numerical Mathematics
T1  - Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type
EP  - 488
IS  - 4
SP  - 478
VL  - 4
DO  - 10.4208/nmtma.2011.m103
ER  - 

@article{
author = "Stanić, Marija P. and Cvetković, Aleksandar",
year = "2011",
abstract = "In this paper we consider polynomials orthogonal with respect to the linear functional L : P -> C, defined on the space of all algebraic polynomials P by L[p] = integral(1)(-1)p(x)(1 - x)(alpha-1/2)(1 + x)(beta-1/2)exp(i zeta x)dx, where alpha, beta > 1/2 are real numbers such that l = vertical bar beta - alpha vertical bar is a positive integer, and zeta is an element of R\{0}. We prove the existence of such orthogonal polynomials for some pairs of alpha and zeta and for all nonnegative integers l. For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference relations. For such orthogonal polynomials the corresponding quadrature rules of Gaussian type are considered. Also, some numerical examples are included.",
publisher = "Global Science Press",
journal = "Numerical Mathematics",
title = "Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type",
pages = "488-478",
number = "4",
volume = "4",
doi = "10.4208/nmtma.2011.m103"
}

Stanić, M. P.,& Cvetković, A.. (2011). Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type. in Numerical Mathematics
Global Science Press., 4(4), 478-488.
https://doi.org/10.4208/nmtma.2011.m103

Stanić MP, Cvetković A. Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type. in Numerical Mathematics. 2011;4(4):478-488.
doi:10.4208/nmtma.2011.m103 .

Stanić, Marija P., Cvetković, Aleksandar, "Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type" in Numerical Mathematics, 4, no. 4 (2011):478-488,
https://doi.org/10.4208/nmtma.2011.m103 . .

TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Cvetković, Aleksandar
AU  - Stanić, Marija P.
PY  - 2011
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/1239
AB  - A generalized N-point Birkhoff-Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived.
PB  - Elsevier Science Inc, New York
T2  - Applied Mathematics and Computation
T1  - A generalized Birkhoff-Young-Chebyshev quadrature formula for analytic functions
EP  - 948
IS  - 3
SP  - 944
VL  - 218
DO  - 10.1016/j.amc.2011.02.007
ER  - 

@article{
author = "Milovanović, Gradimir V. and Cvetković, Aleksandar and Stanić, Marija P.",
year = "2011",
abstract = "A generalized N-point Birkhoff-Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived.",
publisher = "Elsevier Science Inc, New York",
journal = "Applied Mathematics and Computation",
title = "A generalized Birkhoff-Young-Chebyshev quadrature formula for analytic functions",
pages = "948-944",
number = "3",
volume = "218",
doi = "10.1016/j.amc.2011.02.007"
}

Milovanović, G. V., Cvetković, A.,& Stanić, M. P.. (2011). A generalized Birkhoff-Young-Chebyshev quadrature formula for analytic functions. in Applied Mathematics and Computation
Elsevier Science Inc, New York., 218(3), 944-948.
https://doi.org/10.1016/j.amc.2011.02.007

Milovanović GV, Cvetković A, Stanić MP. A generalized Birkhoff-Young-Chebyshev quadrature formula for analytic functions. in Applied Mathematics and Computation. 2011;218(3):944-948.
doi:10.1016/j.amc.2011.02.007 .

Milovanović, Gradimir V., Cvetković, Aleksandar, Stanić, Marija P., "A generalized Birkhoff-Young-Chebyshev quadrature formula for analytic functions" in Applied Mathematics and Computation, 218, no. 3 (2011):944-948,
https://doi.org/10.1016/j.amc.2011.02.007 . .