凸集的均匀凸性模数

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-07-20 DOI:10.1007/s00013-024-02031-8

Carlo Alberto De Bernardi, Libor Veselý

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引用次数: 0

摘要

我们为 C 定义了四种凸性模的变体，并证明它们都是重合的。对于 \(C=B_X\)（X 的单位球）来说，这个结果是经典且众所周知的，与 \(B_X.\)的特殊情况相比，这个结果的证明并不那么容易。我们还证明了，如果 C 的凸模不等同于空，那么 C 是有界的。这扩展了 M.V. Balashov 和 D. Repovš 的一个结果。

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Moduli of uniform convexity for convex sets

Let C be a proper, closed subset with nonempty interior in a normed space X. We define four variants of modulus of convexity for C and prove that they all coincide. This result, which is classical and well-known for \(C=B_X\) (the unit ball of X), requires a less easy proof than the particular case of \(B_X.\) We also show that if the modulus of convexity of C is not identically null, then C is bounded. This extends a result by M.V. Balashov and D. Repovš.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.