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

Khamsanga Sinsongkham, Watchareepan Atiponrat

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.