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<p>We investigate the zero-finding problem for operators that satisfy a broader class of monotone conditions. We propose dynamical systems and establish ergodic convergence under monotonicity, as well as weak and strong convergence results under cocoercivity, in both continuous- and discrete-time settings. Our results not only refine and extend existing results in the area, but also demonstrate applicability in scenarios where current theory faces limitations. The theoretical results are illustrated and validated through examples.</p>

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Finding zeros of generalized monotone operators via first-order dynamical systems

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Pham Viet Hai,
  • Trinh Ngoc Hai

摘要

We investigate the zero-finding problem for operators that satisfy a broader class of monotone conditions. We propose dynamical systems and establish ergodic convergence under monotonicity, as well as weak and strong convergence results under cocoercivity, in both continuous- and discrete-time settings. Our results not only refine and extend existing results in the area, but also demonstrate applicability in scenarios where current theory faces limitations. The theoretical results are illustrated and validated through examples.