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<p>In this manuscript, we use the PV iterative method to approximate the fixed points of Reich-Suzuki-type nonexpansive mappings. We establish both weak and strong convergence results for the PV iterative scheme. Numerical experiments are conducted to compare the performance of the PV iteration with other iteration methods. Additionally, we provide an application of our methodology by transforming absolute value equations into a fixed-point problem. Finally, we include polynomiographic visualizations to illustrate and compare the convergence behavior of different iterative methods applied to complex polynomial equations.</p>

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Convergence of the PV iteration for Reich–Suzuki type nonexpansive mappings with applications to Absolute value equations and Polynomiography

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Pragati Gautam,
  • Vineet

摘要

In this manuscript, we use the PV iterative method to approximate the fixed points of Reich-Suzuki-type nonexpansive mappings. We establish both weak and strong convergence results for the PV iterative scheme. Numerical experiments are conducted to compare the performance of the PV iteration with other iteration methods. Additionally, we provide an application of our methodology by transforming absolute value equations into a fixed-point problem. Finally, we include polynomiographic visualizations to illustrate and compare the convergence behavior of different iterative methods applied to complex polynomial equations.