A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings
<p/> <p>We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality proble...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/232163 |
| _version_ | 1819010234936459264 |
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| author | Wu Soon-Yi Fan Gang-Lun Peng Jian-Wen |
| author_facet | Wu Soon-Yi Fan Gang-Lun Peng Jian-Wen |
| author_sort | Wu Soon-Yi |
| collection | DOAJ |
| description | <p/> <p>We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone and <inline-formula> <graphic file="1687-1812-2011-232163-i1.gif"/></inline-formula>-Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative sequences generated by these processes are obtained. The results in this paper extend and improve some known results in the literature.</p> |
| first_indexed | 2024-12-21T01:09:02Z |
| format | Article |
| id | doaj.art-83412457ed3a4d5aa4e1b40c36f5fc2f |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-21T01:09:02Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-83412457ed3a4d5aa4e1b40c36f5fc2f2022-12-21T19:20:58ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122011-01-0120111232163A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone MappingsWu Soon-YiFan Gang-LunPeng Jian-Wen<p/> <p>We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone and <inline-formula> <graphic file="1687-1812-2011-232163-i1.gif"/></inline-formula>-Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative sequences generated by these processes are obtained. The results in this paper extend and improve some known results in the literature.</p>http://www.fixedpointtheoryandapplications.com/content/2011/232163 |
| spellingShingle | Wu Soon-Yi Fan Gang-Lun Peng Jian-Wen A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings Fixed Point Theory and Applications |
| title | A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings |
| title_full | A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings |
| title_fullStr | A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings |
| title_full_unstemmed | A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings |
| title_short | A Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings |
| title_sort | hybrid extragradient scheme for system of equilibrium problems nonexpansive mappings and monotone mappings |
| url | http://www.fixedpointtheoryandapplications.com/content/2011/232163 |
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