Convergence of a new three-step iteration process to common fixed points of three G-nonexpansive mappings in Banach spaces with directed graphs

In this paper, from some confusions in examples on the convergence of certain iteration processes in the literature, we introduce the coordinate-convexity to study the convergence of a new three-step iteration process in Banach spaces with directed graphs. We prove some comparison results of the rate of convergence of the proposed iteration process and certain iteration processes for G-contractive mappings. We also prove the weak and strong convergence results for three G-nonexpansive mappings, and give three numerical examples to illustrate the obtained results.