Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 350483, 10 pages
Research Article

An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Shenghua Wang, Lanxiang Yu, and Baohua Guo

School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China

Received 6 May 2008; Accepted 24 August 2008

Academic Editor: William Kirk

Copyright © 2008 Shenghua 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 K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let {Ti}i=1 be an infinite countable family of asymptotically nonexpansive mappings with the sequence {kin} satisfying kin1 for each i=1,2,, n=1,2,, and limnkin=1 for each i=1,2,. In this paper, we introduce a new implicit iterative scheme generated by {Ti}i=1 and prove that the scheme converges strongly to a common fixed point of {Ti}i=1, which solves some certain variational inequality.