Skip to main content

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

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

Affiliations

Authors

Corresponding author

Correspondence to C. E. Chidume.

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.

Reprints and Permissions

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

Download citation

Keywords

  • Variational Inequality
  • Nonexpansive Mapping
  • Full Article
  • Publisher Note
\