Weak and strong convergence of a two-step iterations for a finite family of generalized asymptotically quasi-nonexpansive mappings

Abstract

In this paper, we introduce and study a new two-step iterative scheme to approximate common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings. We establish several strong and weak convergence results of the proposed algorithm in Banach spaces. These results generalize and refine many known results in the current literature.