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Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems

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  • Kasamsuk Ungchittrakool

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
    Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

  • Somyot Plubtieng

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
    Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

  • Natthaphon Artsawang

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
    Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

  • Purit Thammasiri

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

Abstract

In this paper, we introduce and study a modified Mann-type algorithm that combines inertial terms for solving common fixed point problems of two countable families of nonexpansive mappings in Hilbert spaces. Under appropriate assumptions on the sequences of parameters, we establish a strong convergence result for the sequence generated by the proposed method in finding a common fixed point of two countable families of nonexpansive mappings. This method can be applied to solve the monotone inclusion problem. Additionally, we employ a modified Mann-type iterative algorithm to address image restoration problems. Furthermore, we present numerical results across different scenarios to demonstrate the superior efficiency of our algorithm compared to existing algorithms.

Suggested Citation

  • Kasamsuk Ungchittrakool & Somyot Plubtieng & Natthaphon Artsawang & Purit Thammasiri, 2023. "Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems," Mathematics, MDPI, vol. 11(13), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2927-:d:1183039
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    References listed on IDEAS

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    1. Kamonrat Nammanee & Suthep Suantai & Prasit Cholamjiak, 2012. "A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, April.
    2. Li-Jun Zhu & Yonghong Yao, 2023. "Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    3. Mohammad Akram & Mohammad Dilshad & Arvind Kumar Rajpoot & Feeroz Babu & Rais Ahmad & Jen-Chih Yao, 2022. "Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    4. Prasit Cholamjiak & Suthep Suantai, 2012. "Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions," Journal of Global Optimization, Springer, vol. 54(1), pages 185-197, September.
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