Criteria for Convexity of Closed Sets in Banach Spaces

被引：1
作者：
Ledyaev, Yuri S. [1 ]
机构：
[1] Western Michigan Univ, Dept Math, Kalamazoo, MI 49008 USA
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2019年 / 304卷 / 01期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1134/S0081543819010139
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Criteria for the convexity of closed sets in general Banach spaces in terms of the Clarke and Bouligand tangent cones are proved. In the case of uniformly convex spaces, these convexity criteria are stated in terms of proximal normal cones. These criteria are used to derive sufficient conditions for the convexity of the images of convex sets under nonlinear mappings and multifunctions.
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页码：190 / 204
页数：15
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