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<p>This work introduces a novel modified Halpern-type proximal point algorithm, designed for a finite family of <i>k</i>-demimetric mappings, resolvents of monotone operators, and resolvents of mixed equilibrium problems. In the context of Hadamard spaces, we establish the convergence of the perturbed algorithm to a common zero of the finite family of mixed equilibrium problems and monotone operators, as well as to a common fixed point of the finite family of <i>k</i>-demimetric mappings. Furthermore, we provide a numerical example to illustrate the effectiveness of the proposed algorithm.</p>

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Modified proximal-type algorithms for solving multi-structured problems in Hadamard spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月20日

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  • Athar Abbas,
  • Somayya Komal,
  • Muhammad Jabir Khan,
  • Hafiz Fukhar-ud-din,
  • Muhammad Aqeel Ahmad Khan

摘要

This work introduces a novel modified Halpern-type proximal point algorithm, designed for a finite family of k-demimetric mappings, resolvents of monotone operators, and resolvents of mixed equilibrium problems. In the context of Hadamard spaces, we establish the convergence of the perturbed algorithm to a common zero of the finite family of mixed equilibrium problems and monotone operators, as well as to a common fixed point of the finite family of k-demimetric mappings. Furthermore, we provide a numerical example to illustrate the effectiveness of the proposed algorithm.