Best proximity coincidence point theorem for G-proximal generalized auxiliary function in a metric space with Graph G

Abstract

We study best proximity coincidence points of a pair of mappings that is G- proximal generalized auxiliary function in a complete metric space endowed with a directed graph G and prove that if any pair of two best proximity coincidence points is an edge of the graph G, then the best proximity coincidence points is unique. Besides, we give an example and corollaries relevant to our main theorem.