Fixed Point Theorems for a New Class of Mappings in Modular Spaces Endowed with a Graph

In this paper, we discuss a class of mappings more general than ρ-nonexpansive mapping defined on a modular space endowed with a graph. In our investigation, we prove the existence of fixed point results of these mappings. Then, we also introduce an iterative scheme for which proves the convergence to a fixed point of such mapping in a modular space with a graph.