Best Proximity Point Results for G-Proximal Geraghty Mappings

Let $(X,d)$ be a complete metric space endowed with a graph $G.$We introduce a new type of  Geraghty contractions which are $G$-proximal. Best proximity theorems for these mappings in $X$ are given as well as an example supporting the main result. Moreover, we obtain several consequences which generalize other results in the literature.