Fixed point theorems for a new class of mappings in modular spaces endowed with a graph (Q2198040)

Summary: In this paper, we discuss a class of mappings more general than \(\rho \)-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.