Open Access 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

Author Affiliations

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

For all author emails, please log on.

Fixed Point Theory and Applications 2008, 2008:350483  doi:10.1155/2008/350483


The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2008/1/350483


Received: 6 May 2008
Accepted: 24 August 2008
Published: 28 August 2008

© 2008 The Author(s).

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 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.

Publisher note

To access the full article, please see PDF.