The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces
We show a necessary and sufficient condition for the existence of metric projection on a class of half-space Kx0*,c={x∈X:x*(x)≤c} in Banach space. Two representations of metric projections PKx0*,c and PKx0,c are given, respectively, where Kx0,c stands for dual half-space of Kx0*,c in dual space X*....
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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/10.1155/2014/908676 |
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| _version_ | 1849468904274919424 |
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| author | Zihou Zhang Chunyan Liu |
| author_facet | Zihou Zhang Chunyan Liu |
| author_sort | Zihou Zhang |
| collection | DOAJ |
| description | We show a necessary and sufficient condition for the existence of metric projection on a class of half-space Kx0*,c={x∈X:x*(x)≤c} in Banach space. Two representations of metric projections PKx0*,c and PKx0,c are given, respectively, where Kx0,c stands for dual half-space of Kx0*,c in dual space X*. By these representations, a series of continuity results of the metric projections PKx0*,c and PKx0,c are given. We also provide the characterization that a metric projection is a linear bounded operator. |
| format | Article |
| id | doaj-art-ff71a14df71d4c248c23866a3ac0f8da |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ff71a14df71d4c248c23866a3ac0f8da2025-08-20T03:25:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/908676908676The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach SpacesZihou Zhang0Chunyan Liu1College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, ChinaCollege of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, ChinaWe show a necessary and sufficient condition for the existence of metric projection on a class of half-space Kx0*,c={x∈X:x*(x)≤c} in Banach space. Two representations of metric projections PKx0*,c and PKx0,c are given, respectively, where Kx0,c stands for dual half-space of Kx0*,c in dual space X*. By these representations, a series of continuity results of the metric projections PKx0*,c and PKx0,c are given. We also provide the characterization that a metric projection is a linear bounded operator.http://dx.doi.org/10.1155/2014/908676 |
| spellingShingle | Zihou Zhang Chunyan Liu The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces Abstract and Applied Analysis |
| title | The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces |
| title_full | The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces |
| title_fullStr | The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces |
| title_full_unstemmed | The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces |
| title_short | The Representations and Continuity of the Metric Projections on Two Classes of Half-Spaces in Banach Spaces |
| title_sort | representations and continuity of the metric projections on two classes of half spaces in banach spaces |
| url | http://dx.doi.org/10.1155/2014/908676 |
| work_keys_str_mv | AT zihouzhang therepresentationsandcontinuityofthemetricprojectionsontwoclassesofhalfspacesinbanachspaces AT chunyanliu therepresentationsandcontinuityofthemetricprojectionsontwoclassesofhalfspacesinbanachspaces AT zihouzhang representationsandcontinuityofthemetricprojectionsontwoclassesofhalfspacesinbanachspaces AT chunyanliu representationsandcontinuityofthemetricprojectionsontwoclassesofhalfspacesinbanachspaces |