Convergence Theorems for Common Fixed Points of Two G-Nonexpansive Mappings in a Banach Space with a Directed Graph

Abstract

The purpose of this paper is to prove weak and strong convergence theorems of a new iterative scheme for common fixed points of  two $G$-nonexpansive mappings in a Banach space  endowed with a directed graph.  Also, we give an example for  numerical result of our main theorem and compare the rate of convergence of our iteration and Ishikawa iteration. Furthermore, we give some consequences of those theorems for two monotone nonexpansive mappings in a Banach space.