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

Anchalee Khemphet

Abstract

In this work, we present a result on the existence of a best proximity coincidence point of a pair of mappings that is a $G$-proximal generalized Geraghty mapping in a complete metric space endowed with a directed graph $G$. Furthermore, if any pair of the two best proximity coincidence points is an edge of the graph $G$, then the best proximity coincidence point is unique. In addition, an example is given to support the main theorem. Finally, we provide some consequences of the theorem for the special cases of the mapping.