Mann Iteration Process for Monotone Nonexpansive Mappings with a Graph

Abstract

Let $(X,\Vert .\Vert )$ be a Banach space. Let $C$ be a nonempty, bounded, closed, and convex subset of $X$ and $T:C\to C$ be a $G$-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by $$x_{n+1}=t_{n}T(x_n)+(1-t_n)x_n,n=1,2,\cdots$$ can be proved the existence of a fixed point of $G$-monotone nonexpansive mappings.

Accepted, Georgian Mathematical Journal 2016