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<p>In the context of modular function spaces, we propose and investigate the Fibonacci-Ishikawa iteration method applied to non-expansive, asymptotically monotonic mathematical operators. We establish both <i>ω</i>-convergence and <i>ω</i>-almost everywhere convergence of the Fibonacci-Ishikawa sequence, thereby extending several existing results in the literature. Furthermore, our findings highlight the convergence behavior of the sequence toward its <i>ω</i>-almost everywhere limit, particularly as it relates to the minimizing sequence of a given function. Also, a comparative analysis with classical Mann and Ishikawa iteration methods reveals that the Fibonacci-Ishikawa iteration exhibits superior convergence properties, rapidly approaching the fixed point in significantly fewer iterations. Finally, we discuss the possible applicability of practical relevance.</p>

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Fibonacci-Ishikawa iterative method in modular spaces for asymptotically non-expansive monotonic mathematical operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月17日

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  • Anita Tomar,
  • Khairul Habib Alam,
  • Mohammad Sajid,
  • Yumnam Rohen,
  • S. Surendra Singh

摘要

In the context of modular function spaces, we propose and investigate the Fibonacci-Ishikawa iteration method applied to non-expansive, asymptotically monotonic mathematical operators. We establish both ω-convergence and ω-almost everywhere convergence of the Fibonacci-Ishikawa sequence, thereby extending several existing results in the literature. Furthermore, our findings highlight the convergence behavior of the sequence toward its ω-almost everywhere limit, particularly as it relates to the minimizing sequence of a given function. Also, a comparative analysis with classical Mann and Ishikawa iteration methods reveals that the Fibonacci-Ishikawa iteration exhibits superior convergence properties, rapidly approaching the fixed point in significantly fewer iterations. Finally, we discuss the possible applicability of practical relevance.