Journal of Optimization Theory and Applications

, Volume 128, Issue 1, pp 191–201

Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings

  • N. Nadezhkina
  • W. Takahashi
Article

DOI: 10.1007/s10957-005-7564-z

Cite this article as:
Nadezhkina, N. & Takahashi, W. J Optim Theory Appl (2006) 128: 191. doi:10.1007/s10957-005-7564-z

Abstract

In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process

Keywords

Extragradient methodfixed pointsmonotone mappingsnonexpansive mappingsvariational inequalities

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • N. Nadezhkina
    • 1
  • W. Takahashi
    • 2
  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan