Some critical remarks on recent results concerning \(\digamma-\)contractions in \(b-\)metric spaces

Mudasir Younis; Nikola Mirkov; Ana Savić; Mirjana Pantović; Stojan Radenović

doi:10.56754/0719-0646.2501.057

DOI:

https://doi.org/10.56754/0719-0646.2501.057

Abstract

This paper aims to correct recent results on a generalized class of \(\digamma-\)contractions in the context of \(b-\)metric spaces. The significant work consists of repairing some novel results involving \(\digamma-\)contraction within the structure of \(b\)-metric spaces. Our objective is to take advantage of the property \((F1)\) instead of the four properties viz. \((F1)\), \((F2)\), \((F3)\) and \((F4)\) applied in the results of Nazam et al. [Coincidence and common fixed point theorems for four mappings satisfying \((\alpha_s,F)-\)contraction", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664–690, 2018]. Our approach of proving the results utilizing only the condition \((F1)\) enriches, improves, and condenses the proofs of a multitude of results in the existing state-of-art.

Mathematics Subject Classification:

54H25 , 47H10 , 65F15

Mudasir Younis Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India. https://orcid.org/0000-0001-5499-4272
Nikola Mirkov University of Belgrade, "Vinča" Institute of Nuclear Sciences - National Institute of the Republic of Serbia, Mike Petrovića Alasa 12–14, 11351 Belgrade, Republic of Serbia. https://orcid.org/0000-0002-3057-9784
Ana Savić School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, Vojode Stepe 283, 11010 Belgrade, Serbia. https://orcid.org/0000-0002-8099-1136
Mirjana Pantović Department of Mathematics and Informatics, University of Kragujevac, Faculty of Science Radoja Domanovica 12, 34000 Kragujevac, Serbia. https://orcid.org/0000-0001-6257-8666
Stojan Radenović University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Republic of Serbia. https://orcid.org/0000-0001-8254-6688

Pages: 57–66
Date Published: 2023-04-24
Vol. 25 No. 1 (2023)

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