On Stability of Fixed Points for Multi-Valued Mappings with an Application
This paper studies the stability of fixed points for multi-valued mappings in relation to selections. For multi-valued mappings admitting Michael selections, some examples are given to show that the fixed point mapping of these mappings are neither upper semi-continuous nor almost lower semi-continu...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/978257 |
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| _version_ | 1850166199069966336 |
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| author | Qi-Qing Song |
| author_facet | Qi-Qing Song |
| author_sort | Qi-Qing Song |
| collection | DOAJ |
| description | This paper studies the stability of fixed points for multi-valued mappings in relation to selections. For multi-valued mappings admitting Michael selections, some examples are given to show that the fixed point mapping of these mappings are neither upper semi-continuous nor almost lower semi-continuous. Though the set of fixed points may be not compact for multi-valued mappings admitting Lipschitz selections, by finding sub-mappings of such mappings, the existence of minimal essential sets of fixed points is proved, and we show that there exists at least an essentially stable fixed point for almost all these mappings. As an application, we deduce an essentially stable result for differential inclusion problems. |
| format | Article |
| id | doaj-art-dd8cbc288d3c4ff89ba48b24faa64220 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dd8cbc288d3c4ff89ba48b24faa642202025-08-20T02:21:30ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/978257978257On Stability of Fixed Points for Multi-Valued Mappings with an ApplicationQi-Qing Song0College of Science, Guilin University of Technology, Guilin 541004, ChinaThis paper studies the stability of fixed points for multi-valued mappings in relation to selections. For multi-valued mappings admitting Michael selections, some examples are given to show that the fixed point mapping of these mappings are neither upper semi-continuous nor almost lower semi-continuous. Though the set of fixed points may be not compact for multi-valued mappings admitting Lipschitz selections, by finding sub-mappings of such mappings, the existence of minimal essential sets of fixed points is proved, and we show that there exists at least an essentially stable fixed point for almost all these mappings. As an application, we deduce an essentially stable result for differential inclusion problems.http://dx.doi.org/10.1155/2014/978257 |
| spellingShingle | Qi-Qing Song On Stability of Fixed Points for Multi-Valued Mappings with an Application Abstract and Applied Analysis |
| title | On Stability of Fixed Points for Multi-Valued Mappings with an Application |
| title_full | On Stability of Fixed Points for Multi-Valued Mappings with an Application |
| title_fullStr | On Stability of Fixed Points for Multi-Valued Mappings with an Application |
| title_full_unstemmed | On Stability of Fixed Points for Multi-Valued Mappings with an Application |
| title_short | On Stability of Fixed Points for Multi-Valued Mappings with an Application |
| title_sort | on stability of fixed points for multi valued mappings with an application |
| url | http://dx.doi.org/10.1155/2014/978257 |
| work_keys_str_mv | AT qiqingsong onstabilityoffixedpointsformultivaluedmappingswithanapplication |