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<p>In this work, we present a contraction-type method with an inertia term and line-search rule to solve monotone inclusion problems and the fixed point problems. We also get the result that the sequences are convergent strongly without requiring to know the Lipschitz-type constant. Finally, some numerical applications show the effectiveness of our proposed algorithms.</p>

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Contraction-type method with line-search rule for solving monotone inclusion problems and fixed point problems in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Linan Wang,
  • Gang Cai,
  • Yi Huang,
  • Qiao-Li Dong

摘要

In this work, we present a contraction-type method with an inertia term and line-search rule to solve monotone inclusion problems and the fixed point problems. We also get the result that the sequences are convergent strongly without requiring to know the Lipschitz-type constant. Finally, some numerical applications show the effectiveness of our proposed algorithms.