文献类型：期刊文献

中文题名：Banach空间中线性流形上的度量投影的表达式

英文题名：The Representive of Metric Projection on the Linear Manifold in Arbitary Banach Space

作者：倪仁兴[1]

机构：[1]绍兴文理学院数学系

年份：2005

卷号：25

期号：1

起止页码：99

中文期刊名：数学研究与评论：英文版

收录：CSTPCD、、北大核心2004、CSCD2011_2012、北大核心、CSCD

基金：国家自然科学基金(10271025)浙江省自然科学基金(102002)

语种：中文

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

外文关键词：Banach space; normalized duality mapping; linear manifold; representive of metric projec- tion; necessary and sufficient condition

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.

外文摘要：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.