Fixed point theorem for a Meir-Keeler type mapping in a metric space with a transitive relation

TL;DR

This paper establishes fixed point theorems for Meir-Keeler type mappings within metric spaces that have a transitive relation, expanding the theoretical framework for such mappings.

Contribution

It introduces new fixed point results for Meir-Keeler type mappings in metric spaces with transitive relations, generalizing existing fixed point theorems.

Findings

Characterization of Meir-Keeler type mappings

Fixed point theorem in metric spaces with transitive relation

Extension of fixed point results to new mapping classes

Abstract

The aim of this paper is to provide characterizations of a Meir-Keeler type mapping and a fixed point theorem for the mapping in a metric space endowed with a transitive relation.