Local characterization of strongly convex sets
Local characterization of strongly convex sets
复制标题
强凸集的局部表征
DOI：
10.1016/j.jmaa.2012.10.071
复制
发表时间：
2012
影响因子：
1.3
通讯作者：
G. Reissig
中科院分区：
文献类型：
--
作者：
Alexander Weber;G. Reissig
用局部性质刻画了Hilbert空间中的强凸集。用于此目的的一个量是集合δΩ的凸性模Ω的推广。我们还证明了LIMε→0δΩ(ε)/ε2只要Ω是闭的和凸的就存在。
Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity δΩof a set Ω. We also show that limε→0δΩ(ε)/ε2exists whenever Ω is closed and convex.