A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings
The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of stri...
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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/10.1155/2012/804642 |
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| _version_ | 1832566776402018304 |
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| author | Yaqin Wang Hongkun Xu Xiaoli Fang |
| author_facet | Yaqin Wang Hongkun Xu Xiaoli Fang |
| author_sort | Yaqin Wang |
| collection | DOAJ |
| description | The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan (2010) and many others. |
| format | Article |
| id | doaj-art-a52e28dc8168465c926cbc66c6796371 |
| 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-a52e28dc8168465c926cbc66c67963712025-02-03T01:03:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/804642804642A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive MappingsYaqin Wang0Hongkun Xu1Xiaoli Fang2Department of Mathematics, Shaoxing University, Shaoxing 312000, ChinaDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, TaiwanDepartment of Mathematics, Shaoxing University, Shaoxing 312000, ChinaThe purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan (2010) and many others.http://dx.doi.org/10.1155/2012/804642 |
| spellingShingle | Yaqin Wang Hongkun Xu Xiaoli Fang A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings Journal of Applied Mathematics |
| title | A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings |
| title_full | A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings |
| title_fullStr | A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings |
| title_full_unstemmed | A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings |
| title_short | A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings |
| title_sort | hybrid extragradient like method for variational inequalities equilibrium problems and an infinitely family of strictly pseudocontractive mappings |
| url | http://dx.doi.org/10.1155/2012/804642 |
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