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A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

Author

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  • Kamonrat Nammanee
  • Suthep Suantai
  • Prasit Cholamjiak

Abstract

We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping ð ½ ð œ‘ , where 𠜑 is a gauge function on [ 0 , ∞ ) . Our results improve and extend those announced by G. Marino and H.-K. Xu (2006) and many authors.

Suggested Citation

  • Kamonrat Nammanee & Suthep Suantai & Prasit Cholamjiak, 2012. "A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, April.
    • Handle: RePEc:hin:jnljam:506976
    DOI: 10.1155/2012/506976
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    Cited by:

    1. 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.

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