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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Fenghui Wang,
  • Hai Yu

摘要

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.