Best Proximity Coincidence Point Theorem for G-proximal Generalized Geraghty Auxiliary Function in a Metric Space with Graph G

Abstract

In a complete metric space endowed with a directed graph G, we investigate the best proximity coincidence points of a pair of mappings that is G-proximal generalized auxiliary function. We show that the best proximity coincidence point is unique if any pair of two best proximity coincidence points is an edge of the graph G. In addition, we provide an example as well as corollaries that are pertinent to our main theorem.