Open Access

Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities

Journal of Inequalities and Applications20072008:284345

DOI: 10.1155/2008/284345

Received: 3 July 2007

Accepted: 17 October 2007

Published: 3 December 2007

Abstract

Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
The Abdus Salam International Centre for Theoretical Physics
(2)
Department of Mathematics and Statistics, College of Sciences and Mathematics, Auburn University
(3)
Department of Mathematical Sciences, Bayero University

Copyright

© C. E. Chidume 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.