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An Adaptive and Expanded Framework For Multiple-Operator Split Common Fixed Point Problems

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  • Fenghui Wang

    (Luoyang Normal University)

  • Hai Yu

    (Luoyang Normal University)

Abstract

This paper addresses the multiple-operator split common fixed point problem, a fundamental challenge with wide applications in signal processing and medical imaging. We propose new block iterative algorithms, extending existing approaches to handle more demicontractive operators. Our key contributions are: firstly, introducing adaptive step-size mechanisms that remove the need to estimate the norm of linear operators; secondly, developing extrapolated Landweber operators to enhance convergence; and thirdly, formulating a double cyclic projection method to enhance flexibility and efficiency. We establish the weak convergence of these methods under intermittent activation of operator blocks through theoretical analysis. Numerical experiments demonstrate the algorithms’ effectiveness and efficiency in solving tough problems.

Suggested Citation

  • Fenghui Wang & Hai Yu, 2025. "An Adaptive and Expanded Framework For Multiple-Operator Split Common Fixed Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-25, October.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:1:d:10.1007_s10957-025-02765-7
    DOI: 10.1007/s10957-025-02765-7
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    References listed on IDEAS

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    1. Andrzej Cegielski, 2015. "General Method for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 385-404, May.
    2. Meng Wen & Jigen Peng & Yuchao Tang, 2015. "A Cyclic and Simultaneous Iterative Method for Solving the Multiple-Sets Split Feasibility Problem," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 844-860, September.
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