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<p>This study presents a novel class of iterative methods for approximating the fixed points of a contractive-like mapping. We examine the applicability of the proposed family to different problems, including Fisher’s equation, and analyze its stability and strong convergence characteristics. Based on existing iterative operators, it is shown that the proposed multi-step class is equivalent to the Mann iteration, and vice versa. Moreover, numerical examples demonstrate that the proposed technique performs better than some three-step approaches that have been used and described in the literature. These results demonstrate the potential of the proposed iterative family.</p>

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A novel iterative class for computing fixed points based on contractive-like operators with applications to the Fisher–KPP equation

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Munish Kansal,
  • Hemant Kumar Nashine,
  • Litika Rani

摘要

This study presents a novel class of iterative methods for approximating the fixed points of a contractive-like mapping. We examine the applicability of the proposed family to different problems, including Fisher’s equation, and analyze its stability and strong convergence characteristics. Based on existing iterative operators, it is shown that the proposed multi-step class is equivalent to the Mann iteration, and vice versa. Moreover, numerical examples demonstrate that the proposed technique performs better than some three-step approaches that have been used and described in the literature. These results demonstrate the potential of the proposed iterative family.