A new interpretation of Djoković's inequality (Q2708296)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new interpretation of Djoković's inequality |
scientific article |
Statements
13 January 2002
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inequalities
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Banach space
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Hilbert space
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Djoković inequality
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Hlawka space
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A new interpretation of Djoković's inequality (English)
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One of the results offered states that a Banach space, on which the inequality NEWLINE\[NEWLINE\sum_{1\leq j_1< \dots <j_k\leq n}\|x_{j_1}+ \dots +x_{j_k}\|\leq \binom{n-2}{k-1} \sum_{j=1 }^n\|x_j\|+ \binom{n-2}{k-2} \Biggl\|\sum_{j=1}^n x_j \Biggr\|NEWLINE\]NEWLINE [\textit{D. Ž. Djoković}, Period. Math.-Phys. Astron. (2) 18, 169-175 (1963; Zbl 0127.32503)] holds, is a ``Hlawka-space'' in the sense that \(\|x+y\|+\|y+z\|+\|z+x\|\leq \|x\|+\|y\|+\|z\|+\|x+y+z\|\) is satisfied.
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