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Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings

Author

Listed:
  • Najla Altwaijry

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

  • Tahani Aldhaban

    (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)

  • Hong-Kun Xu

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

Abstract

We show that the viscosity approximation method coupled with the Krasnoselskii–Mann iteration generates a sequence that strongly converges to a fixed point of a given nonexpansive mapping in the setting of uniformly smooth Banach spaces. Our result shows that the geometric property (i.e., uniform smoothness) of the underlying space plays a role in relaxing the conditions on the choice of regularization parameters and step sizes in iterative methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1153-:d:384215
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    References listed on IDEAS

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    1. 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.
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