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Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem

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Abstract

In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem in a Hilbert space. Then, we show that one of the sequences converges strongly and the other converges weakly.

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Authors and Affiliations

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

    A. Tada & W. Takahashi

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  1. A. Tada
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  2. W. Takahashi
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Correspondence to W. Takahashi.

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Communicated by R. Glowinski.

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Tada, A., Takahashi, W. Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem. J Optim Theory Appl 133, 359–370 (2007). https://doi.org/10.1007/s10957-007-9187-z

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  • DOI: https://doi.org/10.1007/s10957-007-9187-z

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