Results 1 to 10 of about 675,466 (153)

Inequalities of Gauß-Minkowski type

1997
An 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., Pecaric, Josip, Varosanec, Sanja   +2 more
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Orlicz–Brunn–Minkowski inequalities for Blaschke–Minkowski homomorphisms

Geometriae Dedicata, 2016
The paper is concerned with Brunn-Minkowski-type inequalities for Blaschke-Minkowski homomorphisms and their polars with respect to Orlicz addition.
Chen, Feixiang, Leng, Gangsong
openaire   +2 more sources

A Brunn–Minkowski-Type Inequality

Geometriae Dedicata, 1999
For 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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More on reverses of Minkowski’s inequalities and Hardy’s integral inequalities

Asian-European Journal of Mathematics, 2018
In 2012, Sulaiman [Reverses of Minkowski’s, Hölder’s, and Hardy’s integral inequalities, Int. J. Mod. Math. Sci. 1(1) (2012) 14–24] proved integral inequalities concerning reverses of Minkowski’s and Hardy’s inequalities.
B. Benaissa
semanticscholar   +1 more source

On a Discrete Brunn--Minkowski Type Inequality

SIAM Journal on Discrete Mathematics, 2018
The 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, David Iglesias, Jesús Yepes Nicolás   +2 more
openaire   +1 more source

Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

Fundamenta Mathematicae, 1993
Let be an arbitrary bijection of R+. We prove that if the two-place function 1 ( (s) + (t)) is subadditive in R 2 then must be a convex homeomorphism of R+. This is a partial converse of Mulholland's inequality.
J. Matkowski, T. Świątkowski
semanticscholar   +1 more source

Companions to the Brunn–Minkowski inequality

Positivity
Let \(\mathcal{C}\) 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, 1984
Summary: 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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Brunn-Minkowski inequality

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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Fast full search in motion estimation by hierarchical use of Minkowski's inequality (HUMI)

Pattern Recognition, 1998
Jinyun Lu, Kuang-Shyr Wu, Ja-Chen Lin
semanticscholar   +1 more source