A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems
Abstract This paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP defined with respect to the pseudomonotone bifunction, the fixed point problem (FPP) for...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-08-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03518-2 |
| _version_ | 1818908894912577536 |
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| author | Yasir Arfat Poom Kumam Muhammad Aqeel Ahmad Khan Parinya Sa Ngiamsunthorn Attapol Kaewkhao |
| author_facet | Yasir Arfat Poom Kumam Muhammad Aqeel Ahmad Khan Parinya Sa Ngiamsunthorn Attapol Kaewkhao |
| author_sort | Yasir Arfat |
| collection | DOAJ |
| description | Abstract This paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP defined with respect to the pseudomonotone bifunction, the fixed point problem (FPP) for a finite family of -demicontractive operators, and the split null point problem. From the numerical standpoint, combining various classical iterative algorithms to study two or more abstract problems is a fascinating field of research. We, therefore, propose an iterative algorithm that combines the parallel hybrid extragradient algorithm with the inertial extrapolation technique. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under a suitable set of constraints and numerical results. |
| first_indexed | 2024-12-19T22:18:16Z |
| format | Article |
| id | doaj.art-bc5bdcd8d2254c209ec26672f38cdda6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T22:18:16Z |
| publishDate | 2021-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-bc5bdcd8d2254c209ec26672f38cdda62022-12-21T20:03:42ZengSpringerOpenAdvances in Difference Equations1687-18472021-08-012021111910.1186/s13662-021-03518-2A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problemsYasir Arfat0Poom Kumam1Muhammad Aqeel Ahmad Khan2Parinya Sa Ngiamsunthorn3Attapol Kaewkhao4KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculity of Science, King Mongkut’s University of Technology Thonburi (KMUTT)KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculity of Science, King Mongkut’s University of Technology Thonburi (KMUTT)Department of Mathematics, COMSATS University IslamabadCenter of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT)Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai UniversityAbstract This paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP defined with respect to the pseudomonotone bifunction, the fixed point problem (FPP) for a finite family of -demicontractive operators, and the split null point problem. From the numerical standpoint, combining various classical iterative algorithms to study two or more abstract problems is a fascinating field of research. We, therefore, propose an iterative algorithm that combines the parallel hybrid extragradient algorithm with the inertial extrapolation technique. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under a suitable set of constraints and numerical results.https://doi.org/10.1186/s13662-021-03518-2Parallel hybrid algorithmInertial extrapolation techniquePseudomonotone equilibrium problemFixed point problemNull point problem |
| spellingShingle | Yasir Arfat Poom Kumam Muhammad Aqeel Ahmad Khan Parinya Sa Ngiamsunthorn Attapol Kaewkhao A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems Advances in Difference Equations Parallel hybrid algorithm Inertial extrapolation technique Pseudomonotone equilibrium problem Fixed point problem Null point problem |
| title | A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems |
| title_full | A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems |
| title_fullStr | A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems |
| title_full_unstemmed | A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems |
| title_short | A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems |
| title_sort | parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium fixed point and split null point problems |
| topic | Parallel hybrid algorithm Inertial extrapolation technique Pseudomonotone equilibrium problem Fixed point problem Null point problem |
| url | https://doi.org/10.1186/s13662-021-03518-2 |
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