Weak and Strong Convergence Theorems of G-Monotone Nonexpansive Mapping in Banach Spaces with a Graph.

In this article, we introduce a faster iteration for finding a fixed point of G-monotone nonexpansive mapping in a uniformly convex Banach space with a directed graph. We establish weak and strong convergence theorems of fixed point for G-monotone nonexpansive mapping with a more convenient G-convex interval instead of the previous fixed point dominated conditions in convergence analysis. Moreover, we provide two numerical examples to illustrate the convergence behavior and advantages of the proposed method. [ABSTRACT FROM AUTHOR]