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Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions

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Abstract

We first investigate strong convergence of the sequence generated by implicit and explicit viscosity approximation methods for a one-parameter nonexpansive semigroup in a real Banach space E which has a uniformly Gâteaux differentiable norm and admits the duality mapping j φ , where φ is a gauge function on [0, ∞). The main results also improve and extend some known results concerning the normalized duality mapping in the literature.

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Authors and Affiliations

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

    Prasit Cholamjiak

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

    Suthep Suantai

  3. 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. Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions. J Glob Optim 54, 185–197 (2012). https://doi.org/10.1007/s10898-011-9756-4

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  • DOI: https://doi.org/10.1007/s10898-011-9756-4

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