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A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications

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  • Suthep Suantai

    (Research Group in Mathematics and Applied Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Kunrada Kankam

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Damrongsak Yambangwai

    (School of Science, University of Phayao, Phayao 56000, Thailand)

  • Watcharaporn Cholamjiak

    (School of Science, University of Phayao, Phayao 56000, Thailand)

Abstract

In this work, we aim to prove the strong convergence of the sequence generated by the modified inertial parallel viscosity-type algorithm for finding a common fixed point of a finite family of nonexpansive mappings under mild conditions in real Hilbert spaces. Moreover, we present the numerical experiments to solve linear systems and differential problems using Gauss–Seidel, weight Jacobi, and successive over relaxation methods. Furthermore, we provide our algorithm to show the efficiency and implementation of the LASSO problems in signal recovery. The novelty of our algorithm is that we show that the algorithm is efficient compared with the existing algorithms.

Suggested Citation

  • Suthep Suantai & Kunrada Kankam & Damrongsak Yambangwai & Watcharaporn Cholamjiak, 2022. "A Modified Inertial Parallel Viscosity-Type Algorithm for a Finite Family of Nonexpansive Mappings and Its Applications," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4422-:d:982238
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    References listed on IDEAS

    as
    1. Suthep Suantai & Kunrada Kankam & Watcharaporn Cholamjiak & Watcharaporn Yajai, 2022. "Parallel Hybrid Algorithms for a Finite Family of G -Nonexpansive Mappings and Its Application in a Novel Signal Recovery," Mathematics, MDPI, vol. 10(12), pages 1-16, June.
    2. Cholamjiak, Watcharaporn & Dutta, Hemen, 2022. "Viscosity modification with parallel inertial two steps forward-backward splitting methods for inclusion problems applied to signal recovery," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    Full references (including those not matched with items on IDEAS)

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