| 倪仁兴.Banach空间中线性流形上的度量投影的表达式[J].数学研究及应用,2005,25(1):99~103 |
| Banach空间中线性流形上的度量投影的表达式 |
| The Representive of Metric Projection on the Linear Manifold in Arbitary Banach Space |
| 投稿时间：2002-09-16 |
| DOI：10.3770/j.issn:1000-341X.2005.01.014 |
| 中文关键词: Banach空间 正规对偶映射 线性流形 度量投影表达式 充要条件 |
| 英文关键词:Banach space normalized duality mapping linear manifold representive of metric projec- tion necessary and sufficient condition |
| 基金项目:国家自然科学基金(10271025),浙江省自然科学基金(102002) |
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| 中文摘要: |
| 借助于正规对偶映射,建立了一般Banach空间中线性流形上的(集值)度量投影存在的 充要条件,同时给出了度量投影的表达式和点到线性流形上的距离公式.这些本质地推广和改进了 王玉文和于金凤在空间自反、严格凸和光滑强假定下的相应结果. |
| 英文摘要: |
| This paper established the necessary and sufficient condition for existence of (set-valued) metric projection on the linear manifold in arbitary Banach space by the normalized duality mapping. Meanwhile, a representive of metric projection on the linear manifold in arbitary Banach space was given, so was the distance formulas from a point to the linear manifold in Banach space. These indeed extended and improved the corresponding results obtained by Wang Yuwen and Yu Jinfeng under the strong assumption that the space X was a reflexive, smooth and strictly convex Banach space. |
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