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<p>In this paper, we present and examine the split monotone variational inclusion problem (SMVIP) related to maximal monotone operators in Hilbert spaces. With the help of Tikhonov’s regularization and viscosity approximation technique, we develop and discuss an iterative scheme for computing feasible solutions to the SMVIP under appropriate control conditions. The strong convergence and effectiveness of the proposed algorithm are demonstrated through both theoretical analysis and numerical results, including real-world applications, respectively. We highlight the key advantages of our iterative scheme in comparison to existing algorithms for the SMVIP. The findings presented in this paper enhance various existing results in the current literature.</p>

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Some variants of regularized splitting method for solving split monotone variational inclusion problems

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Yasir Arfat

摘要

In this paper, we present and examine the split monotone variational inclusion problem (SMVIP) related to maximal monotone operators in Hilbert spaces. With the help of Tikhonov’s regularization and viscosity approximation technique, we develop and discuss an iterative scheme for computing feasible solutions to the SMVIP under appropriate control conditions. The strong convergence and effectiveness of the proposed algorithm are demonstrated through both theoretical analysis and numerical results, including real-world applications, respectively. We highlight the key advantages of our iterative scheme in comparison to existing algorithms for the SMVIP. The findings presented in this paper enhance various existing results in the current literature.