文献类型：期刊文献

中文题名：关于赋范线性空间中Chebyshev中心的存在性

英文题名：On the Existence of Chebyshev Centers in Normed Linear Spaces

作者：倪仁兴[1]

机构：[1]绍兴文理学院数学系

年份：2001

卷号：40

期号：1

起止页码：12

中文期刊名：厦门大学学报：自然科学版

收录：CSTPCD、、北大核心2000、CSCD2011_2012、北大核心、CSCD

基金：国家自然科学基金!资助项目 ( 199710 13)

语种：中文

中文关键词：赋范线性范围;紧局部一致凸空间;极大化序列;极小化序列;CHEBYSHEV中心

外文关键词：incomplete normed linear space; compactly locally uniform round spaces; maximizing (minimizing) sequence; Chebyshev center

中文摘要：讨论了空间的完备性与有中心的赋范线性空间间的关系 ,用构造性的方法证得了有中心的赋范线性空间必完备 ;完备的赋范线性空间未必有中心 .指出不完备 CL UR赋范线性空间 X总有一有界闭凸子集 B,它既无远达点又对 X\B无最佳逼近点 .

外文摘要：The relationship between completeness of spaces and normed linear spaces admitting centers is discussed. By using constructive method, it is proved that a normed linear space admitting centers must be complete and complete normed linear space may not admit center. As a result, it is shown that each imcomplete CLUR normed linear space X contains a closed bounded convex subset B with the following properties: 1) B does not contain any farthest point in X; 2) B does not contain any nearest point to the elements of its complement.