Coupled Fixed Points of monotone mappings in a metric space with a graph

TL;DR

This paper introduces mixed G-monotone mappings in metric spaces with graphs and establishes conditions for coupled fixed points under weak contractivity, expanding fixed point theory in structured spaces.

Contribution

It defines mixed G-monotone mappings in graph-endowed metric spaces and provides new sufficient conditions for coupled fixed points under weak contractivity.

Findings

Established existence of coupled fixed points under new conditions.

Extended fixed point theory to graph-structured metric spaces.

Provided theoretical framework for future applications.

Abstract

In this work, we define the concept of mixed $G$-monotone mappings defined on a metric space endowed with a graph. Then we obtain sufficient conditions for the existence of coupled fixed points for such mappings when a weak contractivity type condition is satisfied.