General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions
Abstract In this paper, we introduce two general iterative methods (one implicit method and one explicit method) for finding a solution of a general system of variational inequalities (GSVI) with the constraints of finitely many generalized mixed equilibrium problems and a fixed point problem of a c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1899-0 |
| _version_ | 1818451412629061632 |
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| author | Qian-Wen Wang Jin-Lin Guan Lu-Chuan Ceng Bing Hu |
| author_facet | Qian-Wen Wang Jin-Lin Guan Lu-Chuan Ceng Bing Hu |
| author_sort | Qian-Wen Wang |
| collection | DOAJ |
| description | Abstract In this paper, we introduce two general iterative methods (one implicit method and one explicit method) for finding a solution of a general system of variational inequalities (GSVI) with the constraints of finitely many generalized mixed equilibrium problems and a fixed point problem of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed implicit and explicit iterative methods to a solution of the GSVI with the above constraints, which is the unique solution of a certain variational inequality. The results presented in this paper improve, extend, and develop the corresponding results in the earlier and recent literature. |
| first_indexed | 2024-12-14T21:06:47Z |
| format | Article |
| id | doaj.art-0afaa9f559f0422f8769d30a2ddbbc0c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-14T21:06:47Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0afaa9f559f0422f8769d30a2ddbbc0c2022-12-21T22:47:23ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-11-012018113510.1186/s13660-018-1899-0General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractionsQian-Wen Wang0Jin-Lin Guan1Lu-Chuan Ceng2Bing Hu3Department of Mathematics, Shanghai Normal UniversityDepartment of Mathematics, Shanghai Normal UniversityDepartment of Mathematics, Shanghai Normal UniversityLAMPS and Department of Mathematics and Statistics, York UniversityAbstract In this paper, we introduce two general iterative methods (one implicit method and one explicit method) for finding a solution of a general system of variational inequalities (GSVI) with the constraints of finitely many generalized mixed equilibrium problems and a fixed point problem of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed implicit and explicit iterative methods to a solution of the GSVI with the above constraints, which is the unique solution of a certain variational inequality. The results presented in this paper improve, extend, and develop the corresponding results in the earlier and recent literature.http://link.springer.com/article/10.1186/s13660-018-1899-0General iterative methodGeneral system of variational inequalitiesContinuous monotone mappingContinuous pseudocontractive mappingVariational inequalityGeneralized mixed equilibrium problem |
| spellingShingle | Qian-Wen Wang Jin-Lin Guan Lu-Chuan Ceng Bing Hu General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions Journal of Inequalities and Applications General iterative method General system of variational inequalities Continuous monotone mapping Continuous pseudocontractive mapping Variational inequality Generalized mixed equilibrium problem |
| title | General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions |
| title_full | General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions |
| title_fullStr | General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions |
| title_full_unstemmed | General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions |
| title_short | General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions |
| title_sort | general iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions |
| topic | General iterative method General system of variational inequalities Continuous monotone mapping Continuous pseudocontractive mapping Variational inequality Generalized mixed equilibrium problem |
| url | http://link.springer.com/article/10.1186/s13660-018-1899-0 |
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