Fixed points of mappings satisfying contractive condition of integral type in modular spaces endowed with a graph

Abstract

Jachymski (Proc. Am. Math. Soc. 136:1359-1373, 2008) gave a modified version of a Banach fixed point theorem on a metric space endowed with a graph. The aim of this paper is to present fixed point results of mappings satisfying integral type contractive conditions in the framework of modular spaces endowed with a graph. Some examples are presented to support the results proved herein. Our results generalize and extend various comparable results in the existing literature.