A Novel Iterative Procedure with Perturbations for Two Generalized Asymptotically Quasi-Nonexpansive Nonself-Mappings in Banach Spaces

Abstract

The goal of this note is to propose a new projection type of two-step iterative procedure with perturbations for finding the common fixed point of two nonself generalized asymptotically quasi-nonexpansive mappings in Banach spaces. A sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is also established in a real uniformly convex Banach space as well as strong convergence theorems in a nonempty closed convex subset of a real Banach space. Our results generalize and improve several relevant results of the existing literature.