Weak and Strong Convergence of a Two-Step Iterations for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings

Hossein Dehghan, Amir Gharajelo

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.

Keywords

Generalized asymptotically quasi-nonexpansive mapping, Mann-type iteration, Ishikawa-type iteration, Uniformly convex Banach space, Common fixed point

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