Approximating Common Fixed Points for Two G-Asymptotically Nonexpansive Mappings with Directed Grahps

Manakorn Wattanataweekul

Abstract

In this paper, we introduce an iterative method for finding a common fixed points of two $G$-asymptotically nonexpansive mappings with directed graph in a uniformly convex Banach space. Weak and strong convergence of the proposed method are established under some suitable control conditions. We also give some numerical example for supporting our main theorem and compare convergence rate between the studied iteration and the modified Ishikawa iteration.