g-approximate best proximity pairs in metric space with a directed graph

TL;DR

This paper establishes conditions for the existence of approximate best proximity pairs in metric spaces equipped with a directed graph, linking graph structure with proximity pair existence.

Contribution

It introduces sufficient conditions for the existence of G-approximate best proximity pairs in metric spaces with an associated directed graph.

Findings

Provides new theoretical conditions for proximity pairs

Connects graph structure with metric space properties

Extends best proximity pair theory to directed graphs

Abstract

Let(X,d) be a metric space that has a directed graph G such that the sets V(G) and E(G) are respectively vertices and edges corresponding to X. We obtain sufficient conditions for the existence of an G-approximate best proximity pair of the mapping T in the metric space X endowed with a graph G such that the set V(G) of vertices of G coincides with X.