G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph
In this article, we introduce the G-Tseng’s extragradient method, inspired by the extragradient method defined by Korpelevich, for solving G-variational inequality problems in Hilbert space. We also address a fixed point problem in a Hilbert space endowed with a graph using the proposed G-Tseng’s ex...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X25000126 |
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| author | Monika Swami M.R. Jadeja |
| author_facet | Monika Swami M.R. Jadeja |
| author_sort | Monika Swami |
| collection | DOAJ |
| description | In this article, we introduce the G-Tseng’s extragradient method, inspired by the extragradient method defined by Korpelevich, for solving G-variational inequality problems in Hilbert space. We also address a fixed point problem in a Hilbert space endowed with a graph using the proposed G-Tseng’s extragradient method. In the context of Hilbert space, we establish weak and strong convergence theorems for the algorithm. Additionally, we provide numerical examples to support our findings. |
| format | Article |
| id | doaj-art-949d5e52bf3d4fafb8debdda459591a1 |
| institution | OA Journals |
| issn | 2666-657X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-949d5e52bf3d4fafb8debdda459591a12025-08-20T02:07:36ZengElsevierExamples and Counterexamples2666-657X2025-06-01710018510.1016/j.exco.2025.100185G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graphMonika Swami0M.R. Jadeja1Department of Mathematics, Atmiya University, Rajkot, 360005, Gujarat, IndiaDepartment of AI, ML and DS, Marwadi University, Rajkot, 360003, Gujarat, India; Corresponding author.In this article, we introduce the G-Tseng’s extragradient method, inspired by the extragradient method defined by Korpelevich, for solving G-variational inequality problems in Hilbert space. We also address a fixed point problem in a Hilbert space endowed with a graph using the proposed G-Tseng’s extragradient method. In the context of Hilbert space, we establish weak and strong convergence theorems for the algorithm. Additionally, we provide numerical examples to support our findings.http://www.sciencedirect.com/science/article/pii/S2666657X25000126-variational inequality problemG-Tseng’s extragradient methodFixed point problemWeak and strong convergence |
| spellingShingle | Monika Swami M.R. Jadeja G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph Examples and Counterexamples -variational inequality problem G-Tseng’s extragradient method Fixed point problem Weak and strong convergence |
| title | G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph |
| title_full | G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph |
| title_fullStr | G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph |
| title_full_unstemmed | G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph |
| title_short | G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph |
| title_sort | g tseng s extragradient method for approximating g variational inequality problem in hilbert space endowed with graph |
| topic | -variational inequality problem G-Tseng’s extragradient method Fixed point problem Weak and strong convergence |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X25000126 |
| work_keys_str_mv | AT monikaswami gtsengsextragradientmethodforapproximatinggvariationalinequalityprobleminhilbertspaceendowedwithgraph AT mrjadeja gtsengsextragradientmethodforapproximatinggvariationalinequalityprobleminhilbertspaceendowedwithgraph |