A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces

Abstract

In this paper, we introduce and study a new iterative algorithm which is a combination of a modified Mann iterative scheme and a generalized explicit methods (GEM) for finding a common fixed points of an infinite family of quasi-nonexpansive mappings in Banach spaces. Under suitable conditions, some strong convergence theorems for finding a common fixed points of an infinite family of quasi-nonexpansive mappings are obtained without imposing any compactness assumption. Presented results improve and generalize many known results in the current literature.