Some fixed point results in metric spaces equipped with a Graph and their applications

Abstract

In this paper, we define the notion of $(F-H)_G$- contraction and utilize the same to obtain fixed point results in the setting of metric spaces equipped with a graph. Our results generalizes many known fixed point results in literature. As an application, we investigate the existence and uniqueness of a solution of integral equation. Finally, some suitable examples are given to validate our claim.