Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces

Abstract

The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real uniformly convex Banach spaces if E satisfies Opial's condition or the dual E * of E has the Kedec-Klee property. Our results extend and improve some known corresponding results from the existing literature. c 2014 All rights reserved.Keywords: Asymptotically quasi-nonexpansive non-self mappings, common fixed point, the modified two-step iteration process with errors for non-self maps, uniformly convex Banach space, weak convergence. 2010 MSC: 47H09, 47H10, 47J25.

Weak convergence theorems for nearly asymptotically nonexpansive mappings and asymptotically nonexpansive non-self mappings in uniformly convex Banach spaces

“…(14) Note that T 1 (PT 1 ) n−1 y n − q ≤ l n y n − q ≤ h n y n − q By virtue of (11), we find that lim sup…”

Common Fixed Point of a Finite-step Iteration Algorithm Under Total Asymptotically Quasi-nonexpansive Maps

“…Therefore, it is important to determine whether an iteration algorithm converges to fixed point of a map. In this field, there are numerous works regarding convergence of various iteration methods, as one can see in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13). Let be a Banach space, B subset of M and be a selfmap of with set of all fixed points ( ).…”