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Strong convergence theorems by hybrid methods for nonexpansive mappings with equilibrium problems in Banach spaces equilibrium problems in Banach spaces

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Advances in Mathematical Economics

Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 14))

Abstract

Our purpose in this paper is to prove strong convergence theorems by hybrid methods for nonexpansive mappings in a Banach space under appropriate conditions. We first prove a strong convergence theorem by the shrinking projection method for semi-positively homogeneous nonexpansive mappings with an equilibrium problem in a Banach space. Next, we obtain another strong convergence theorem by the monotone hybrid method for semi-positively homogeneous nonexpansive mappings with an equilibrium problem in a Banach space. These theorems are proved by using the concept of set convergence.

Received: January 11, 2010

Revised: July 9, 2010

JEL classification: C62, C68

Mathematics Subject Classification (2000): 47H05, 47H09, 47H20

The research of the first author and the second author was partially supported by Grant-in-Aid for Scientific Research No. 19540167 from Japan Society for the Promotion of Science and by the grant NSC 98-2115-M-110-001, respectively.

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Authors and Affiliations

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

    Wataru Takahashi

  2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan

    Wataru Takahashi & Jen-Chih Yao

Authors
  1. Wataru Takahashi
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    Toru Maruyama (Professor) (Professor)

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Takahashi, W., Yao, JC. (2011). Strong convergence theorems by hybrid methods for nonexpansive mappings with equilibrium problems in Banach spaces equilibrium problems in Banach spaces. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 14. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53883-7_9

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