Approximation of best proximity pair for noncyclic relatively ρ-nonexpansive mappings in modular spaces endowed with a graph

Abstract

In this work, at first we prove an existence result of best proximity pair for noncyclic relatively ρ-nonexpansive mapping in the setting of modular spaces endowed with a convex directed graph. Furthermore, we study the convergence of a pair of sequences ((x_n, x’_n ))n generated by a new iterative scheme for noncyclic relatively (ρG)-nonexpansive mapping in uniformly convex modular spaces equipped with a convex directed graph.