Convexity of generalized proximinal sets in Banach spaces

被引：0

作者：

Luo, Xian-Fa ^{[1
]}

Li, Chong ^{[2
]}

Peng, Lihui ^{[3
]}

Yao, Jen-Chih ^{[4
]}

机构：

[1] China Jiliang Univ, Dept Math, Hangzhou, Zhejiang, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou, Zhejiang, Peoples R China

[3] Zhejiang Gongshang Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

[4] China Med Univ, Ctr Gen Educ, Taichung, Taiwan

来源：

OPTIMIZATION | 2018年 / 67卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Generalized best approximation; proximinal set; weakly* uniform convexity; compactly locally uniform convexity; CHEBYSHEV SETS; TIME FUNCTION;

D O I：

10.1080/02331934.2018.1480626

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

For a bounded closed convex subset C of a Banach space X with the origin as an interior point, we study the convexity issue of proximinal sets G in Banach spaces in the sense of generalized best approximation determined by the Minkowski functional generated by C. Some sufficient conditions such as the smoothness and compactly locally uniform convexity of C, or the weakly* uniform convexity of C. are provided for a proximinal set G to be convex.

引用

页码：1535 / 1551

页数：17

共 18 条

[1] CRITERIA FOR CONVEXITY OF GENERALIZED CHEBYSHEV SETS IN BANACH SPACES
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[2] Characterizations of Generalized Proximinal Subspaces in Real Banach Spaces
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[10] Weakly convex and proximally smooth sets in Banach spaces
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