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Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces

Fixed Point Theory and Applications volume 2005, Article number: 906783 (2005) Cite this article

Abstract

We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.

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Authors and Affiliations

  1. Department of Mathematics, Shibaura Institute of Technology, Fukasaku, Minuma-ku, Saitama-City, Saitama, 337-8570, Japan

    Sachiko Atsushiba

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Wataru Takahashi

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  1. Sachiko Atsushiba
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  2. Wataru Takahashi
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Correspondence to Sachiko Atsushiba.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Atsushiba, S., Takahashi, W. Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces. Fixed Point Theory Appl 2005, 906783 (2005). https://doi.org/10.1155/FPTA.2005.343

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  • DOI: https://doi.org/10.1155/FPTA.2005.343