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 theor...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/165053 |
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| _version_ | 1832556752122413056 |
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| author | Dezhou Kong Lishan Liu Yonghong Wu |
| author_facet | Dezhou Kong Lishan Liu Yonghong Wu |
| author_sort | Dezhou Kong |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-7cc44c406f2843248db660e3f0b36cbf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7cc44c406f2843248db660e3f0b36cbf2025-02-03T05:44:25ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/165053165053The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach SpacesDezhou Kong0Lishan Liu1Yonghong Wu2 School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, AustraliaWe 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.http://dx.doi.org/10.1155/2015/165053 |
| spellingShingle | Dezhou Kong Lishan Liu Yonghong Wu The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces Abstract and Applied Analysis |
| 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://dx.doi.org/10.1155/2015/165053 |
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