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<p>In this paper, we aim to investigate a newly modified self-adaptive two-subgradient extragradient algorithm that incorporates an inertial effect. This algorithm’s sequence approximates a solution to generalized split feasibility problems involving a non-expansive mapping and a uniformly continuous and pseudo-monotone mapping in real Hilbert spaces. We demonstrate the strong convergence of the sequence generated by our algorithm. Additionally, we apply the proven theorem to approximate solutions for certain nonlinear analysis and optimization problems. Numerical examples are provided to illustrate the impact of the inertial term in our algorithm compared to a similar recent algorithm without the inertial term. Ultimately, our theorem represents a significant improvement, extension, and unification of recent related results in the literature.</p>

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A self-adaptive two-subgradient extragradient algorithm for approximating solutions of generalized split feasibility problems with applications

  • 期刊论文

  • 发表日期：

    2025年4月23日

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  • Monday Ogudu Nnakwe,
  • Masuzyo Mwanza,
  • Abubakar Adamu

摘要

In this paper, we aim to investigate a newly modified self-adaptive two-subgradient extragradient algorithm that incorporates an inertial effect. This algorithm’s sequence approximates a solution to generalized split feasibility problems involving a non-expansive mapping and a uniformly continuous and pseudo-monotone mapping in real Hilbert spaces. We demonstrate the strong convergence of the sequence generated by our algorithm. Additionally, we apply the proven theorem to approximate solutions for certain nonlinear analysis and optimization problems. Numerical examples are provided to illustrate the impact of the inertial term in our algorithm compared to a similar recent algorithm without the inertial term. Ultimately, our theorem represents a significant improvement, extension, and unification of recent related results in the literature.