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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。
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.
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.
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