Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 678519, 9 pages
Research Article

Hybrid Iteration Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings in Banach Spaces

College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

Received 5 December 2008; Revised 3 February 2009; Accepted 9 March 2009

Academic Editor: Joaquim J. Júdice

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.


Let E be a real uniformly convex Banach space, and let{Ti:iI} be N nonexpansive mappings from E into itself with F={xE:Tix=x,iI}ϕ, where I={1,2,,N}. From an arbitrary initial point x1E, hybrid iteration scheme {xn} is defined as follows: xn+1=αnxn+(1αn)(Tnxnλn+1μA(Tnxn)), n1, where A:EE is an L-Lipschitzian mapping, Tn=Ti, i=n(modN), 1iN, 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:iI} 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).