Skip to main content

Advertisement

We’d like to understand how you use our websites in order to improve them. Register your interest.

A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Abstract

A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.

Publisher note

To access the full article, please see PDF.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Suthep Suantai.

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

Klin-eam, C., Suantai, S. A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings. J Inequal Appl 2009, 520301 (2009). https://doi.org/10.1155/2009/520301

Download citation

Keywords

  • Hilbert Space
  • Approximation Method
  • Variational Inequality
  • Convergence Theorem
  • Monotone Mapping