Strong convergence theorems for split variational inequality problems in Hilbert spaces
In this paper, we consider the variational inequality problem and the split common fixed point problem. Considering the common fixed points of an infinite family of nonexpansive mappings, instead of just the fixed point of one nonexpansive mapping, we generalize the results of Tian and Jiang. By rem...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231396?viewType=HTML |
| _version_ | 1827793561942228992 |
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| author | Wenlong Sun Gang Lu Yuanfeng Jin Zufeng Peng |
| author_facet | Wenlong Sun Gang Lu Yuanfeng Jin Zufeng Peng |
| author_sort | Wenlong Sun |
| collection | DOAJ |
| description | In this paper, we consider the variational inequality problem and the split common fixed point problem. Considering the common fixed points of an infinite family of nonexpansive mappings, instead of just the fixed point of one nonexpansive mapping, we generalize the results of Tian and Jiang. By removing a projection operator, we improve the efficiency of our algorithm. Finally, we propose a very simple modification to the extragradient method, which gives our algorithm strong convergence properties. We also provide some numerical examples to illustrate our main results. |
| first_indexed | 2024-03-11T18:20:17Z |
| format | Article |
| id | doaj.art-927ec8fbeeba428c859e351bbf137a35 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T18:20:17Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-927ec8fbeeba428c859e351bbf137a352023-10-16T01:29:02ZengAIMS PressAIMS Mathematics2473-69882023-09-01811272912730810.3934/math.20231396Strong convergence theorems for split variational inequality problems in Hilbert spacesWenlong Sun0Gang Lu 1Yuanfeng Jin 2Zufeng Peng31. Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110870, China 2. Department of Mathematics, Yanbian University, Yanji 133001, China 3. Liaoning Provincial Key Laboratory of Composite Metal Nanomaterials and Magnetic Technology, Shenyang University of Technology, Shenyang 110870, China4. Division of Foundational Teaching, Guangzhou College of Technology and Business, Guangzhou 510850, China2. Department of Mathematics, Yanbian University, Yanji 133001, China5. Department of Mathematics, School of Science, Northeastern University, Shenyang 110819, ChinaIn this paper, we consider the variational inequality problem and the split common fixed point problem. Considering the common fixed points of an infinite family of nonexpansive mappings, instead of just the fixed point of one nonexpansive mapping, we generalize the results of Tian and Jiang. By removing a projection operator, we improve the efficiency of our algorithm. Finally, we propose a very simple modification to the extragradient method, which gives our algorithm strong convergence properties. We also provide some numerical examples to illustrate our main results.https://www.aimspress.com/article/doi/10.3934/math.20231396?viewType=HTMLsplit common fixed pointvariational inequality problemnonexpansive mapping |
| spellingShingle | Wenlong Sun Gang Lu Yuanfeng Jin Zufeng Peng Strong convergence theorems for split variational inequality problems in Hilbert spaces AIMS Mathematics split common fixed point variational inequality problem nonexpansive mapping |
| title | Strong convergence theorems for split variational inequality problems in Hilbert spaces |
| title_full | Strong convergence theorems for split variational inequality problems in Hilbert spaces |
| title_fullStr | Strong convergence theorems for split variational inequality problems in Hilbert spaces |
| title_full_unstemmed | Strong convergence theorems for split variational inequality problems in Hilbert spaces |
| title_short | Strong convergence theorems for split variational inequality problems in Hilbert spaces |
| title_sort | strong convergence theorems for split variational inequality problems in hilbert spaces |
| topic | split common fixed point variational inequality problem nonexpansive mapping |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231396?viewType=HTML |
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