A Strong Convergence Theorem by a New Hybrid Method for an Equilibrium Problem with Nonlinear Mappings in a Hilbert Space

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Abstract

In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for a monotone mapping and the set of fixed points of a nonexpansive mapping in a Hilbert space by using a new hybrid method. Using this theorem, we obtain three new results for finding a solution of an equilibrium problem, a solution of the variational inequality for a monotone mapping and a fixed point of a nonexpansive mapping in a Hilbert space.

Keywords

Hilbert space , equilibrium problem , nonexpansive mapping , inverse-strongly monotone mapping , iteration , strong convergence theorem
  • Rinko Shinzato Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152-8552, Japan.
  • Wataru Takahashi Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152-8552, Japan.
  • Pages: 15–26
  • Date Published: 2008-12-01
  • Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal

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Published

2008-12-01

How to Cite

[1]
R. Shinzato and W. Takahashi, “A Strong Convergence Theorem by a New Hybrid Method for an Equilibrium Problem with Nonlinear Mappings in a Hilbert Space”, CUBO, vol. 10, no. 4, pp. 15–26, Dec. 2008.

Issue

Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal

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Articles