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On Reverse Minkowski-Type Inequalities
Mediterranean Journal of Mathematics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhao, C, Cheung, WS
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Convexity and Minkowski's Inequality
The American Mathematical Monthly, 2005(2005). Convexity and Minkowski's Inequality. The American Mathematical Monthly: Vol. 112, No. 8, pp. 740-742.
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Inequalities of Gauß-Minkowski type
1997An integral version of Ostrowski"s inequality is given. Also, some other generalization of that inequality in connection with Gauss" and Minkowski"s type inequalities are given.
Pearce, Charles E. M. +2 more
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Orlicz–Brunn–Minkowski inequalities for Blaschke–Minkowski homomorphisms
Geometriae Dedicata, 2016The paper is concerned with Brunn-Minkowski-type inequalities for Blaschke-Minkowski homomorphisms and their polars with respect to Orlicz addition.
Chen, Feixiang, Leng, Gangsong
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A Brunn–Minkowski-Type Inequality
Geometriae Dedicata, 1999For convex bodies \(K,L\) in \(\mathbb{R}^n\), let \(M(K,L): =\max_{x\in \mathbb{R}^n}|K\cap(x+L)|\) (where \(|\cdot|\) denotes volume). The author conjectures that \[ |K+L |^{1/n}\geq M(K,L)^{1/n} +{|K |^{1/n} |L|^{1/n}\over M(K,L)^{1/n}}, \] which would be a useful improvement of the Brunn-Minkowski theorem.
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On a Discrete Brunn--Minkowski Type Inequality
SIAM Journal on Discrete Mathematics, 2018The classical Brunn-Minkowski inequality for the Minkowski sum of two compact sets \(K\) and \(L\) in \(\mathbb R^n\) states that \[ \mathrm{vol}(K+L)^{1/n} \geq\mathrm{vol}(K)^{1/n} + \mathrm{vol}(L)^{1/n}. \] On the other hand, if \(A\) and \(B\) are finite subsets of \(\mathbb R^n\) and \(|\;|\) stands for their cardinality, a direct discrete ...
María A. Hernández Cifre +2 more
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Companions to the Brunn–Minkowski inequality
PositivityLet \(\mathcal{C}\) be the family of all compact convex sets in \(\mathbb{R}^n\). For \(A, B \in \mathcal{C}\) denote by \(\operatorname{Vol}(A)\) the Lebesque measure of \(A\) and by \(\Delta (A,B) = \big[\operatorname{Vol}(A)\big]^{1/n} + \big[\operatorname{Vol}(B)\big]^{1/n} - \big[\operatorname{Vol}(A + B)\big]^{1/n}\). An \((m + 1)\)-tuple \((B_0,
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On the similarity of the entropy power inequality and the Brunn- Minkowski inequality (Corresp.)
IEEE Transactions on Information Theory, 1984Summary: The entropy power inequality states that the effective variance (entropy power) of the sum of two independent random variables is greater than the sum of their effective variances. The Brunn-Minkowski inequality states that the effective radius of the set sum of two sets is greater than the sum of their effective radii. Both these inequalities
Max H. M. Costa, Thomas M. Cover
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2000
This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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Hölder’s Inequality, Minkowski’s Inequality and Their Variants
2012In this chapter we’ll introduce two very useful inequalities with broad practical usage: Holder’s inequality and Minkowski’s inequality. We’ll also present few variants of these inequalities. For that purpose we will firstly introduce the following theorem.
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