A new modified three-step iteration method for G-nonexpansive mappings in Banach spaces with a graph

Abstract

In the present article, we establish weak and strong convergence theorems of a new modified three-step iteration method for three G-nonexpansive mappings in a uniformly convex Banach space with a directed graph. Moreover, weak convergence theorem without making use of the Opial’s condition is proved. We also show the numerical experiment for supporting our main results and comparing rate of convergence of the new modified three-step iteration with the three-step Noor iteration and the SP iteration. We also provide some numerical examples to illustrate the convergence behavior and advantages of the proposed method. Furthermore, we apply our results to find solutions of constrained minimization problems and split feasibility problems.