Open Journal of Mathematical Analysis
Vol. 8 (2024), Issue 1, pp. 1 – 17
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2024.0131

Coincidence point results for relational-theoretic contraction mappings in metric spaces with applications

Muhammed Raji\(^{1}\) Arvind Kumar Rajpoot\(^{2}\), Laxmi Rathour\(^{3,*}\), Lakshmi Narayan Mishra\(^{4}\) and Vishnu Narayan Mishra\(^{5}\)
\(^{1}\) Department of Mathematics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
\(^{2}\) Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
\(^{3}\) Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl 796 012, Mizoram, India
\(^{4}\) Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India
\(^{5}\) Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

Copyright © 2024 Muhammed Raji, Arvind Kumar Rajpoot, Laxmi Rathour, Lakshmi Narayan Mishra and Vishnu Narayan Mishra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: May 14, 2024 – Accepted: June 6, 2024 – Published: June 30, 2024

Abstract

In this article, we extend the classic Banach contraction principle to a complete metric space equipped with a binary relation. We accomplish this by generalizing several key notions from metric fixed point theory, such as completeness, closedness, continuity, g-continuity, and compatibility, to the relation-theoretic setting. We then use these generalized concepts to prove results on the existence and uniqueness of coincidence points, defined by two mappings acting on a metric space with a binary relation. As a consequence of our main results, we obtain several established metrical coincidence point theorems. We further provide illustrative examples that~demonstrate~the main results.

Keywords:

Coincidence point; binary relations; \(R\)-completeness; \(R\)-continuity; \(R\)-connected sets; \(d\)-self-closedness.