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<p>This paper presents a family of one-parameter fixed-point iterative schemes based on linear combinations, extending the classical framework of convex combination methods. Building upon this formulation, we propose a three-step iterative scheme that provides a structural generalization of several existing methods in the literature. Under appropriate contractive-type assumptions on Banach spaces, we establish theoretical results, including the strong convergence, stability, and data dependence of the proposed scheme. Numerical experiments on a variety of reference problems illustrate that the proposed method performs competitively with well-known iterative schemes.</p>

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On a class of three-step iterative schemes for fixed points generated via linear combinations

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Manoj Kumar,
  • Puneet Sharma,
  • Ujjwal Thakur,
  • Higinio Ramos,
  • Vinay Kanwar

摘要

This paper presents a family of one-parameter fixed-point iterative schemes based on linear combinations, extending the classical framework of convex combination methods. Building upon this formulation, we propose a three-step iterative scheme that provides a structural generalization of several existing methods in the literature. Under appropriate contractive-type assumptions on Banach spaces, we establish theoretical results, including the strong convergence, stability, and data dependence of the proposed scheme. Numerical experiments on a variety of reference problems illustrate that the proposed method performs competitively with well-known iterative schemes.