The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces
We discuss Ky Fan’s theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of t...
| Main Authors: | , , |
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| Format: | Journal Article |
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Science in China Press
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/42595 |
| _version_ | 1848756463531458560 |
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| author | Liu, Lishan Kong, D. Wu, Yong Hong |
| author_facet | Liu, Lishan Kong, D. Wu, Yong Hong |
| author_sort | Liu, Lishan |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We discuss Ky Fan’s theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors. |
| first_indexed | 2025-11-14T09:12:36Z |
| format | Journal Article |
| id | curtin-20.500.11937-42595 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:12:36Z |
| publishDate | 2015 |
| publisher | Science in China Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-425952017-09-13T14:24:11Z The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces Liu, Lishan Kong, D. Wu, Yong Hong We discuss Ky Fan’s theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors. 2015 Journal Article http://hdl.handle.net/20.500.11937/42595 10.1007/s11425-015-5020-6 Science in China Press restricted |
| spellingShingle | Liu, Lishan Kong, D. Wu, Yong Hong The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces |
| title | The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces |
| title_full | The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces |
| title_fullStr | The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces |
| title_full_unstemmed | The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces |
| title_short | The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces |
| title_sort | best approximation theorems and variational inequalities for discontinuous mappings in banach spaces |
| url | http://hdl.handle.net/20.500.11937/42595 |