Open Access

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

Fixed Point Theory and Applications20082008:350483

https://doi.org/10.1155/2008/350483

Received: 6 May 2008

Accepted: 24 August 2008

Published: 28 August 2008

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.

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Authors’ Affiliations

(1)
School of Mathematics and Physics, North China Electric Power University

Copyright

© ShenghuaWang et al. 2008

This article is published under license to BioMed Central Ltd. 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.