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

Author

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  • Prasit Cholamjiak
  • Suthep Suantai

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. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Prasit Cholamjiak & Suthep Suantai, 2012. "Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions," Journal of Global Optimization, Springer, vol. 54(1), pages 185-197, September.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:185-197
    DOI: 10.1007/s10898-011-9756-4
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    Cited by:

    1. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2021. "Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    2. Kasamsuk Ungchittrakool & Somyot Plubtieng & Natthaphon Artsawang & Purit Thammasiri, 2023. "Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems," Mathematics, MDPI, vol. 11(13), pages 1-21, June.
    3. Suthep Suantai & Kunrada Kankam & Prasit Cholamjiak, 2020. "A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces," Mathematics, MDPI, vol. 8(1), pages 1-13, January.

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