Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”
Апстракт
In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-of-art. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.
Кључне речи:
α-regular with respect to η / Triangular α-admissible / Rectangular metric space / Fixed point / Dynamic programingИзвор:
Nonlinear Analysis: Modelling and Control, 2022, 27, 1, 163-178Издавач:
- Vilnius University Press
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Younis, M. AU - Sretenović, Aleksandra AU - Radenović, Stojan PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3804 AB - In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-of-art. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process. PB - Vilnius University Press T2 - Nonlinear Analysis: Modelling and Control T1 - Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations” EP - 178 IS - 1 SP - 163 VL - 27 DO - 10.15388/NAMC.2022.27.25193 ER -
@article{ author = "Younis, M. and Sretenović, Aleksandra and Radenović, Stojan", year = "2022", abstract = "In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-of-art. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.", publisher = "Vilnius University Press", journal = "Nonlinear Analysis: Modelling and Control", title = "Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”", pages = "178-163", number = "1", volume = "27", doi = "10.15388/NAMC.2022.27.25193" }
Younis, M., Sretenović, A.,& Radenović, S.. (2022). Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”. in Nonlinear Analysis: Modelling and Control Vilnius University Press., 27(1), 163-178. https://doi.org/10.15388/NAMC.2022.27.25193
Younis M, Sretenović A, Radenović S. Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”. in Nonlinear Analysis: Modelling and Control. 2022;27(1):163-178. doi:10.15388/NAMC.2022.27.25193 .
Younis, M., Sretenović, Aleksandra, Radenović, Stojan, "Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”" in Nonlinear Analysis: Modelling and Control, 27, no. 1 (2022):163-178, https://doi.org/10.15388/NAMC.2022.27.25193 . .