Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E.Let Ti:K → K,i = 1,2,...,N,be N uniformly L-Lipschitzian,uniformly asymptotically regular with sequences {ε(ni)} and asymptotically pseudocontractive mappings with sequences {kn(i)},where {kn(i)} and {εn(i)},i = 1,2,...,N,satisfy certain mild conditions.Let a sequence {xn} be generated from x1 ∈ K by zn:=(1-μn)xn+μnTnn xn,xn+1:= λnθnx1+ [1-λn(1 + θn)]xn + λnTnn zn for all integer n 1,where Tn = Tn(modN),and {λn},{θn} and {μn} are three real sequences in [0,1] satisfying appropriate conditions.Then ||xn-Tlxn|| → 0 as n →∞ for each l ∈ {1,2,...,N}.The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye[1],Reinermann[10],Rhoades[11] and Schu[13].
The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].
