Composite Implicit Iteration Process for Two Finite Families of Generalized Asymptotically Quasi-Nonexpansive Mappings

Abstract

In this article, A demiclosed principle is proved for generalized asymptotically nonexpansive mapping in a Banach space. Additionally, it proves strong convergence of a composite implicit iteration scheme to a common fixed point for two finite families of generalized asymptotically quasi-nonexpansive mappings in a nonempty closed convex subset of a uniformly convex Banach space. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. The results of this article improve and extend the corresponding results of Xu and Ori [23], Zhou and Chang [26], Chang et al. [3], Yang and Yu [25], Shahzad and Zegeye [20].