- Research Article
- Open access
- Published:
Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
Journal of Inequalities and Applications volume 2008, Article number: 284345 (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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Chidume, C.E., Chidume, C.O. & Ali, B. Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities. J Inequal Appl 2008, 284345 (2007). https://doi.org/10.1155/2008/284345
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2008/284345