Some critical remarks on “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”
Articles
Mudasir Younis
University Institute of Technology-Rajiv Gandhi Technological University
https://orcid.org/0000-0001-5499-4272
Aleksandra Stretenović
University of Belgrade
https://orcid.org/0000-0003-1152-6377
Stojan Radenović
University of Belgrade
Published 2022-01-01
https://doi.org/10.15388/namc.2022.27.25193
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Keywords

rectangular metric space
triangular alpha-admissible
alpha-regular with respect to eta
dynamic programing
fixed point

How to Cite

Younis M., Stretenović A. and 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’”, Nonlinear Analysis: Modelling and Control, 27(1), pp. 163-178. doi: 10.15388/namc.2022.27.25193.

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-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.

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