Convergence theorems for G-nonexpansive mappings in convex metric spaces with a directed graph

Abstract

We propose the modified Picard–Mann hybrid iterative process for two G-nonexpansive mappings and prove some interesting theorems in the framework of convex metric space endowed with a directed graph. We prove with some numerical examples that our proposed iterative process converges faster than all of Mann, Ishikawa and Noor iterations. Our results generalize and extend several known results to convex metric space endowed with a directed graph, including the results of Khan (Fixed Point Theory Appl 2013:69, 2013).