An algorithm for a class of variational inequalities with the split common fixed point problem with multiple output sets constraints
In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multiple output sets for demicontractive mappings in real Hilbert spaces. The strong convergence of the iterative sequence generat...
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| Published in | Optimization Vol. 74; no. 1; pp. 55 - 79 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
02.01.2025
Taylor & Francis LLC |
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| ISSN | 0233-1934 1029-4945 |
| DOI | 10.1080/02331934.2023.2244174 |
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| Abstract | In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multiple output sets for demicontractive mappings in real Hilbert spaces. The strong convergence of the iterative sequence generated by the algorithm method is established without the prior knowledge of the norms of the given bounded linear operators. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, we include several numerical examples that serve to illustrate the performance of our proposed algorithm. |
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| AbstractList | In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multiple output sets for demicontractive mappings in real Hilbert spaces. The strong convergence of the iterative sequence generated by the algorithm method is established without the prior knowledge of the norms of the given bounded linear operators. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, we include several numerical examples that serve to illustrate the performance of our proposed algorithm. |
| Author | My Van, Le Huynh Viet Anh, Tran |
| Author_xml | – sequence: 1 givenname: Le Huynh surname: My Van fullname: My Van, Le Huynh email: vanlhm@uit.edu.vn, lhmvan.sdh231@hcmut.edu.vn organization: Vietnam National University Ho Chi Minh City – sequence: 2 givenname: Tran surname: Viet Anh fullname: Viet Anh, Tran email: tranvietanh@outlook.com, tvanh@ptit.edu.vn organization: Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology |
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| SubjectTerms | Algorithms demicontractive mapping Fixed points (mathematics) Hilbert space Linear operators split common fixed point problem split common fixed point problem with multiple output sets split feasibility problem with multiple output sets Variational inequality |
| Title | An algorithm for a class of variational inequalities with the split common fixed point problem with multiple output sets constraints |
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