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<p>In this paper, we address a general split inverse problem that involves both a variational inequality with a quasi-monotone and Lipschitz continuous operator and fixed point problems with generalized demimetric mappings in real Hilbert spaces. By utilizing a two-step inertial method and the subgradient extragradient method, we propose an enhanced iterative algorithm that incorporates a novel adaptive non-monotonic step size criterion to effectively solve the general split inverse problem. We establish a strong convergence theorem for this method under standard and mild conditions. Finally, we give some numerical experiments to show the applicability and efficiency of the proposed methods.</p>

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A novel approach to general split inverse problems: addressing quasi-monotone variational inequalities and fixed point problems

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Mohammad Eslamian,
  • Ahmad Kamandi

摘要

In this paper, we address a general split inverse problem that involves both a variational inequality with a quasi-monotone and Lipschitz continuous operator and fixed point problems with generalized demimetric mappings in real Hilbert spaces. By utilizing a two-step inertial method and the subgradient extragradient method, we propose an enhanced iterative algorithm that incorporates a novel adaptive non-monotonic step size criterion to effectively solve the general split inverse problem. We establish a strong convergence theorem for this method under standard and mild conditions. Finally, we give some numerical experiments to show the applicability and efficiency of the proposed methods.