Journal of Optimization Theory and Applications

, Volume 128, Issue 1, pp 191–201 | Cite as

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

  • N. Nadezhkina
  • W. Takahashi


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


Extragradient method fixed points monotone mappings nonexpansive mappings variational inequalities 


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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

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