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Strong Convergence of Mann’s Iteration Process in Banach Spaces

Author

Listed:
  • Hong-Kun Xu

    (School of Science, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Najla Altwaijry

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Souhail Chebbi

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

Mann’s iteration process for finding a fixed point of a nonexpansive mapping in a Banach space is considered. This process is known to converge weakly in some class of infinite-dimensional Banach spaces (e.g., uniformly convex Banach spaces with a Fréchet differentiable norm), but not strongly even in a Hilbert space. Strong convergence is therefore a nontrivial problem. In this paper we provide certain conditions either on the underlying space or on the mapping under investigation so as to guarantee the strong convergence of Mann’s iteration process and its variants.

Suggested Citation

  • Hong-Kun Xu & Najla Altwaijry & Souhail Chebbi, 2020. "Strong Convergence of Mann’s Iteration Process in Banach Spaces," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:954-:d:370010
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    Cited by:

    1. Najla Altwaijry & Tahani Aldhaban & Souhail Chebbi & Hong-Kun Xu, 2020. "Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings," Mathematics, MDPI, vol. 8(7), pages 1-9, July.

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