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

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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

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo, Japan

    N. Nadezhkina

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo, Japan

    W. Takahashi

Authors
  1. N. Nadezhkina
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  2. W. Takahashi
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Communicated by S. Schaible

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Nadezhkina, N., Takahashi, W. Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings. J Optim Theory Appl 128, 191–201 (2006). https://doi.org/10.1007/s10957-005-7564-z

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  • DOI: https://doi.org/10.1007/s10957-005-7564-z

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