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<p>This paper concerns the mixed split feasibility problem in real Hilbert spaces. Employing a constrained optimization approach, we introduce new projection-type algorithms to solve this problem under the assumption that the solution set is nonempty. Our algorithms do not require norm estimates of the transfer operators that appear in each related split problem for implementation, thereby avoiding the difficulties of computing or estimating such norms. Some applications for solving split feasibility problems with multiple output sets and split equality problems are also given. Finally, we provide four numerical examples to illustrate the effectiveness of our proposed algorithms.</p>

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Weak and strong convergence theorems for the mixed split feasibility problem in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • Nguyen Song Ha

摘要

This paper concerns the mixed split feasibility problem in real Hilbert spaces. Employing a constrained optimization approach, we introduce new projection-type algorithms to solve this problem under the assumption that the solution set is nonempty. Our algorithms do not require norm estimates of the transfer operators that appear in each related split problem for implementation, thereby avoiding the difficulties of computing or estimating such norms. Some applications for solving split feasibility problems with multiple output sets and split equality problems are also given. Finally, we provide four numerical examples to illustrate the effectiveness of our proposed algorithms.