Caristi fixed point theorem in metric spaces with a graph and its applications - Phikul Sridarat (2018)
© 2016. The purpose of this paper is to generalize Caristi's fixed point theorem in metric space with a directed graph and w-distance. We discuss Caristi's fixed point theorem for mappings defined on a complete metric space endowed with a directed graph and w-distance and we apply our main result to obtain coupled fixed point theorems in a complete metric space endowed with a directed graph and in a partially ordered complete metric space.