Copyright © 2009 Lin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let E be a real uniformly convex Banach space, and let{Ti:i∈I} be N nonexpansive mappings from E into itself with F={x∈E:Tix=x, i∈I}≠ϕ, where I={1,2,…,N}. From an arbitrary initial point x1∈E, hybrid iteration scheme {xn} is defined as follows: xn+1=αnxn+(1−αn)(Tnxn−λn+1μA(Tnxn)), n≥1, where A:E→E is an L-Lipschitzian mapping, Tn=Ti, i=n(mod N), 1≤i≤N, μ>0, {λn}⊂[0,1), and {αn}⊂[a,b] for some a,b∈(0,1). Under some suitable conditions, the strong and weak convergence theorems of {xn} to a common fixed point of the mappings {Ti:i∈I} are obtained. The results presented in this paper extend and improve the results of Wang (2007) and partially improve the results of Osilike, Isiogugu, and Nwokoro (2007).