Contractive maps in locally transitive relational metric spaces

TL;DR

This paper establishes fixed point results for Meir-Keeler contractive maps within locally transitive relational metric spaces, linking these findings to existing related work.

Contribution

It introduces new fixed point theorems for a specific class of contractive maps in relational metric spaces with local transitivity, expanding the theoretical framework.

Findings

Fixed point results for Meir-Keeler contractive maps.

Connections with prior related fixed point theorems.

Enhanced understanding of contractive maps in relational metric spaces.

Abstract

Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal., Volume 2013, Article ID 259768] are also being discussed.