Some Fixed Point Theorems in Modular Function Spaces Endowed with a Graph

Abstract

The aim of this paper is to give fixed point theorems for $G$-monotone $\rho$-nonexpansive mappings over $\rho$-compact or $\rho$-a.e. compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work.