Iterative solutions via some variants of extragradient approximants in Hilbert spaces
This paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of η-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedd...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-05-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022768?viewType=HTML |
| _version_ | 1811239895810703360 |
|---|---|
| author | Yasir Arfat Muhammad Aqeel Ahmad Khan Poom Kumam Wiyada Kumam Kanokwan Sitthithakerngkiet |
| author_facet | Yasir Arfat Muhammad Aqeel Ahmad Khan Poom Kumam Wiyada Kumam Kanokwan Sitthithakerngkiet |
| author_sort | Yasir Arfat |
| collection | DOAJ |
| description | This paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of η-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedded with the inertial extrapolation technique, the parallel hybrid projection technique and the Halpern iterative methods for the variants. The analysis of the approximants is performed under suitable set of constraints and supported with an appropriate numerical experiment for the viability of the approximants. |
| first_indexed | 2024-04-12T13:09:21Z |
| format | Article |
| id | doaj.art-86f507749343497f949f56ee06dafa10 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T13:09:21Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-86f507749343497f949f56ee06dafa102022-12-22T03:31:55ZengAIMS PressAIMS Mathematics2473-69882022-05-0178139101392610.3934/math.2022768Iterative solutions via some variants of extragradient approximants in Hilbert spacesYasir Arfat 0Muhammad Aqeel Ahmad Khan1Poom Kumam 2Wiyada Kumam3Kanokwan Sitthithakerngkiet41. KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand2. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan 1. KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand3. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand 4. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan5. Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand6. Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok(KMUTNB), 1518, Wongsawang, Bangsue, Bangkok 10800, ThailandThis paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of η-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedded with the inertial extrapolation technique, the parallel hybrid projection technique and the Halpern iterative methods for the variants. The analysis of the approximants is performed under suitable set of constraints and supported with an appropriate numerical experiment for the viability of the approximants.https://www.aimspress.com/article/doi/10.3934/math.2022768?viewType=HTMLinertial extrapolation techniqueparallel hybrid projection technique equilibrium problemfixed point problemstrong convergence |
| spellingShingle | Yasir Arfat Muhammad Aqeel Ahmad Khan Poom Kumam Wiyada Kumam Kanokwan Sitthithakerngkiet Iterative solutions via some variants of extragradient approximants in Hilbert spaces AIMS Mathematics inertial extrapolation technique parallel hybrid projection technique equilibrium problem fixed point problem strong convergence |
| title | Iterative solutions via some variants of extragradient approximants in Hilbert spaces |
| title_full | Iterative solutions via some variants of extragradient approximants in Hilbert spaces |
| title_fullStr | Iterative solutions via some variants of extragradient approximants in Hilbert spaces |
| title_full_unstemmed | Iterative solutions via some variants of extragradient approximants in Hilbert spaces |
| title_short | Iterative solutions via some variants of extragradient approximants in Hilbert spaces |
| title_sort | iterative solutions via some variants of extragradient approximants in hilbert spaces |
| topic | inertial extrapolation technique parallel hybrid projection technique equilibrium problem fixed point problem strong convergence |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022768?viewType=HTML |
| work_keys_str_mv | AT yasirarfat iterativesolutionsviasomevariantsofextragradientapproximantsinhilbertspaces AT muhammadaqeelahmadkhan iterativesolutionsviasomevariantsofextragradientapproximantsinhilbertspaces AT poomkumam iterativesolutionsviasomevariantsofextragradientapproximantsinhilbertspaces AT wiyadakumam iterativesolutionsviasomevariantsofextragradientapproximantsinhilbertspaces AT kanokwansitthithakerngkiet iterativesolutionsviasomevariantsofextragradientapproximantsinhilbertspaces |