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Inertial Krasnoselskii–Mann Method in Banach Spaces

Author

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  • Yekini Shehu

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    These authors contributed equally to this work.)

  • Aviv Gibali

    (Department of Mathematics, ORT Braude College, 2161002 Karmiel, Israel
    The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838 Haifa, Israel
    These authors contributed equally to this work.)

Abstract

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q -uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.

Suggested Citation

  • Yekini Shehu & Aviv Gibali, 2020. "Inertial Krasnoselskii–Mann Method in Banach Spaces," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:638-:d:348607
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    References listed on IDEAS

    as
    1. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    2. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
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