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Journal of Optimization Theory and Applications

, Volume 118, Issue 2, pp 417–428 | Cite as

Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

  • W. Takahashi
  • M. Toyoda
Article

Abstract

In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.

Nonexpansive mappings inverse strongly-monotone mappings variational inequalities fixed points 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • W. Takahashi
    • 1
  • M. Toyoda
    • 1
  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyOh-Okayama, Meguro, TokyoJapan

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