Convergence Theorems of Two-step Iteration Process for Two Asymptotically Quasi-nonexpansive Mappings in the Intermediate Sense

Abstract

In this paper, we establish some weak and strong convergence theorems of modified two-step iteration process for two asymptotically quasi-nonexpansive mappings in the intermediate sense to converge to common fixed points in the setting of real uniformly convex Banach spaces. The results presented in this paper extend, improve and generalize some previous results from the existing literature. Keywords: Asymptotically quasi-nonexpansive mapping in the intermediate sense, modified two-step iteration process, common fixed point, strong convergence, weak convergence, Banach space. 2010 Mathematics Subject Classification: 47H09; 47H10; 47J25.