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Iterative Methods for a Generalized Equilibrium Problem and a Nonexpansive Multi-Valued Mapping

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Abstract

In this paper, we introduce new iterative schemes for approximating common elements of the set of solutions of generalized equilibrium problems and the set of fixed points of nonexpansive multi-valued mappings. We prove some strong convergence theorems of the sequences generated by our iterative process under appropriate additional assumptions in Hilbert spaces. Moreover, we give some numerical results for supporting our main theorem. Our main results improve the corresponding ones obtained in (S. Takahashi, W. Takahashi: Nonlinear Anal. 69: 1025–1033, 2008).

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Acknowledgments

The authors would like to thank University of Phayao and the referees for their remarks that helped us very much in revising the paper.

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Authors and Affiliations

  1. School of Science, University of Phayao, Phayao, 56000, Thailand

    Artit Buangern, Audompong Aeimrun & Watcharaporn Cholamjiak

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  1. Artit Buangern
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  2. Audompong Aeimrun
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  3. Watcharaporn Cholamjiak
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Correspondence to Watcharaporn Cholamjiak.

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Buangern, A., Aeimrun, A. & Cholamjiak, W. Iterative Methods for a Generalized Equilibrium Problem and a Nonexpansive Multi-Valued Mapping. Vietnam J. Math. 45, 477–492 (2017). https://doi.org/10.1007/s10013-016-0225-8

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  • DOI: https://doi.org/10.1007/s10013-016-0225-8

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