Metric Characterizations of α-Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach Spaces
The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of α-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equ...
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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/10.1155/2012/264721 |
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| author | L. C. Ceng Y. C. Lin |
| author_facet | L. C. Ceng Y. C. Lin |
| author_sort | L. C. Ceng |
| collection | DOAJ |
| description | The purpose of this paper is to investigate the problems of the well-posedness
for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of α-well-posedness to the system of mixed quasivariational-like inequalities,
which includes symmetric quasi-equilibrium problems as a special case. Second, we establish
some metric characterizations of α-well-posedness for the system of mixed quasivariational-like
inequalities. Under some suitable conditions, we prove that the α-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like
inequalities. The corresponding concept of α-well-posedness in the generalized sense is also
considered for the system of mixed quasivariational-like inequalities having more than one
solution. The results presented in this paper generalize and improve some known results in
the literature. |
| format | Article |
| id | doaj-art-358f6e09456b48178224d28259a07cea |
| 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-358f6e09456b48178224d28259a07cea2025-02-03T01:07:01ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/264721264721Metric Characterizations of α-Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach SpacesL. C. Ceng0Y. C. Lin1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Occupational Safety and Health, College of Public Health, China Medical University, Taichung 404, TaiwanThe purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of α-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations of α-well-posedness for the system of mixed quasivariational-like inequalities. Under some suitable conditions, we prove that the α-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like inequalities. The corresponding concept of α-well-posedness in the generalized sense is also considered for the system of mixed quasivariational-like inequalities having more than one solution. The results presented in this paper generalize and improve some known results in the literature.http://dx.doi.org/10.1155/2012/264721 |
| spellingShingle | L. C. Ceng Y. C. Lin Metric Characterizations of α-Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach Spaces Journal of Applied Mathematics |
| title | Metric Characterizations of α-Well-Posedness for a System of
Mixed Quasivariational-Like Inequalities in Banach Spaces |
| title_full | Metric Characterizations of α-Well-Posedness for a System of
Mixed Quasivariational-Like Inequalities in Banach Spaces |
| title_fullStr | Metric Characterizations of α-Well-Posedness for a System of
Mixed Quasivariational-Like Inequalities in Banach Spaces |
| title_full_unstemmed | Metric Characterizations of α-Well-Posedness for a System of
Mixed Quasivariational-Like Inequalities in Banach Spaces |
| title_short | Metric Characterizations of α-Well-Posedness for a System of
Mixed Quasivariational-Like Inequalities in Banach Spaces |
| title_sort | metric characterizations of α well posedness for a system of mixed quasivariational like inequalities in banach spaces |
| url | http://dx.doi.org/10.1155/2012/264721 |
| work_keys_str_mv | AT lcceng metriccharacterizationsofawellposednessforasystemofmixedquasivariationallikeinequalitiesinbanachspaces AT yclin metriccharacterizationsofawellposednessforasystemofmixedquasivariationallikeinequalitiesinbanachspaces |