The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces
We prove that Fan's theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point...
| Main Authors: | , , |
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| Format: | Journal Article |
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Hindawi Publishing Corporation
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/41334 |
| _version_ | 1848756116551368704 |
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| author | Kong, D. Liu, Lishan Wu, Yong Hong |
| author_facet | Kong, D. Liu, Lishan Wu, Yong Hong |
| author_sort | Kong, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We prove that Fan's theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors. |
| first_indexed | 2025-11-14T09:07:05Z |
| format | Journal Article |
| id | curtin-20.500.11937-41334 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:07:05Z |
| publishDate | 2015 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-413342017-09-13T14:10:12Z The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces Kong, D. Liu, Lishan Wu, Yong Hong We prove that Fan's theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors. 2015 Journal Article http://hdl.handle.net/20.500.11937/41334 10.1155/2015/165053 Hindawi Publishing Corporation fulltext |
| spellingShingle | Kong, D. Liu, Lishan Wu, Yong Hong The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces |
| title | The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces |
| title_full | The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces |
| title_fullStr | The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces |
| title_full_unstemmed | The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces |
| title_short | The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces |
| title_sort | best approximation theorems and fixed point theorems for discontinuous increasing mappings in banach spaces |
| url | http://hdl.handle.net/20.500.11937/41334 |