A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces

Abstract

In this paper, we proposed a new iterative process to approximate fixed point of generalized $\alpha$-nonexpansivemappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process with other well-known iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized $\alpha$-nonexpansive mappings in a Banach space.

Keywords

• uniformly convex banach space
• weak convergence
• strong convergence
• generalized $alpha$-nonexpansive mapping
• iterative process
• quasi-nonexpansive mapping