Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces
We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establ...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/194509 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561872796123136 |
|---|---|
| author | Lu-Chuan Ceng Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution. |
| format | Article |
| id | doaj-art-c8aef457eea94762873bec3301697434 |
| 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-c8aef457eea94762873bec33016974342025-02-03T01:24:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/194509194509Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach SpacesLu-Chuan Ceng0Ching-Feng Wen1Department of Mathematics, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Shanghai 200234, ChinaCenter for General Education, Kaohsiung Medical University, Kaohsiung 80708, TaiwanWe consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.http://dx.doi.org/10.1155/2012/194509 |
| spellingShingle | Lu-Chuan Ceng Ching-Feng Wen Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces Journal of Applied Mathematics |
| title | Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces |
| title_full | Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces |
| title_fullStr | Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces |
| title_full_unstemmed | Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces |
| title_short | Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces |
| title_sort | well posedness by perturbations of generalized mixed variational inequalities in banach spaces |
| url | http://dx.doi.org/10.1155/2012/194509 |
| work_keys_str_mv | AT luchuanceng wellposednessbyperturbationsofgeneralizedmixedvariationalinequalitiesinbanachspaces AT chingfengwen wellposednessbyperturbationsofgeneralizedmixedvariationalinequalitiesinbanachspaces |