Some convergence results using a new iteration process for generalized nonexpansive mappings in Banach spaces

Abstract

In this paper, we introduce a new iterative process for approximation fixed points. We show the stability of our proposed iteration process. We prove some weak and strong convergence theorems for generalized [Formula: see text]-nonexpansive mappings in the framework of uniformly convex Banach spaces. We also provide an example of a generalized [Formula: see text]-nonexpansive mapping to show numerically that our iteration is faster than various prominent iteration processes.