Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 350483, 10 pages
An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces
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 be a nonempty closed convex subset of a reflexive Banach space with a
weakly continuous dual mapping, and let be an infinite countable family of
asymptotically nonexpansive mappings with the sequence satisfying for
each , , and for each . In this
paper, we introduce a new implicit iterative scheme generated by and prove that
the scheme converges strongly to a common fixed point of , which solves some
certain variational inequality.