Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus
Апстракт
Sharp bounds for cosh(x)/x, sinh(x)/x, and sin(x)/x were obtained, as well as one new bound for e(x)+arctan(x)/root x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann-Liovuille fractional integral and in terms of the standard integral.
Кључне речи:
trigonometric functions / polynomial bounds / L'Hopital's rule of monotonicity / Jordan's inequalityИзвор:
Symmetry, 2022, 14, 6Издавач:
- MDPI, Basel
DOI: 10.3390/sym14061260
ISSN: 2073-8994; 2073-8994
WoS: 000817485700001
Scopus: 2-s2.0-85133738060
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Stojiljković, Vuk AU - Radojević, Slobodan AU - Cetin, Eyup AU - Sesum-Cavić, Vesna AU - Radenović, Stojan PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3717 AB - Sharp bounds for cosh(x)/x, sinh(x)/x, and sin(x)/x were obtained, as well as one new bound for e(x)+arctan(x)/root x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann-Liovuille fractional integral and in terms of the standard integral. PB - MDPI, Basel T2 - Symmetry T1 - Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus IS - 6 VL - 14 DO - 10.3390/sym14061260 ER -
@article{ author = "Stojiljković, Vuk and Radojević, Slobodan and Cetin, Eyup and Sesum-Cavić, Vesna and Radenović, Stojan", year = "2022", abstract = "Sharp bounds for cosh(x)/x, sinh(x)/x, and sin(x)/x were obtained, as well as one new bound for e(x)+arctan(x)/root x. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann-Liovuille fractional integral and in terms of the standard integral.", publisher = "MDPI, Basel", journal = "Symmetry", title = "Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus", number = "6", volume = "14", doi = "10.3390/sym14061260" }
Stojiljković, V., Radojević, S., Cetin, E., Sesum-Cavić, V.,& Radenović, S.. (2022). Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus. in Symmetry MDPI, Basel., 14(6). https://doi.org/10.3390/sym14061260
Stojiljković V, Radojević S, Cetin E, Sesum-Cavić V, Radenović S. Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus. in Symmetry. 2022;14(6). doi:10.3390/sym14061260 .
Stojiljković, Vuk, Radojević, Slobodan, Cetin, Eyup, Sesum-Cavić, Vesna, Radenović, Stojan, "Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus" in Symmetry, 14, no. 6 (2022), https://doi.org/10.3390/sym14061260 . .