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A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces

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Abstract

We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using the concept of the Mosco convergence when the family {T n } satisfies the (*)-condition. The examples of three generated mappings which satisfy the (*)-condition are also given. Using the obtained result, we give some applications concerning the variational inequality problem and the convex minimization problem.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Prasit Cholamjiak & Suthep Suantai

  2. Materials Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Suthep Suantai

Authors
  1. Prasit Cholamjiak
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  2. Suthep Suantai
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Correspondence to Suthep Suantai.

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Cholamjiak, P., Suantai, S. A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces. J Glob Optim 54, 83–100 (2012). https://doi.org/10.1007/s10898-011-9743-9

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  • DOI: https://doi.org/10.1007/s10898-011-9743-9

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