Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems
We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi's hybrid-extragradient method, we pr...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/924309 |
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| _version_ | 1832564039750778880 |
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| author | Lu-Chuan Ceng Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi's hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is proven that three sequences generated by this algorithm converge strongly to the same common solution under very mild conditions. Based on this result, we also construct an iterative algorithm for finding a common fixed point of three mappings, such that one of these mappings is nonexpansive, and the other two mappings are strictly pseudocontractive mappings. |
| format | Article |
| id | doaj-art-05a2c98719cd473db4a69152ea2c1896 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-05a2c98719cd473db4a69152ea2c18962025-02-03T01:11:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/924309924309Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point ProblemsLu-Chuan Ceng0Ching-Feng Wen1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanWe investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi's hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is proven that three sequences generated by this algorithm converge strongly to the same common solution under very mild conditions. Based on this result, we also construct an iterative algorithm for finding a common fixed point of three mappings, such that one of these mappings is nonexpansive, and the other two mappings are strictly pseudocontractive mappings.http://dx.doi.org/10.1155/2012/924309 |
| spellingShingle | Lu-Chuan Ceng Ching-Feng Wen Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems Journal of Applied Mathematics |
| title | Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems |
| title_full | Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems |
| title_fullStr | Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems |
| title_full_unstemmed | Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems |
| title_short | Hybrid Extragradient Iterative Algorithms for Variational Inequalities, Variational Inclusions, and Fixed-Point Problems |
| title_sort | hybrid extragradient iterative algorithms for variational inequalities variational inclusions and fixed point problems |
| url | http://dx.doi.org/10.1155/2012/924309 |
| work_keys_str_mv | AT luchuanceng hybridextragradientiterativealgorithmsforvariationalinequalitiesvariationalinclusionsandfixedpointproblems AT chingfengwen hybridextragradientiterativealgorithmsforvariationalinequalitiesvariationalinclusionsandfixedpointproblems |