Results 211 to 220 of about 1,239,021 (236)

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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Gaussian Brunn-Minkowski Inequalities [PDF]

Transactions of the American Mathematical Society, 2010
A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible
Artem Zvavitch, Richard John Gardner
exaly   +1 more source

On a Discrete Brunn--Minkowski Type Inequality

SIAM Journal on Discrete Mathematics, 2018
The Brunn--Minkowski inequality states that the volume of compact sets $K,L\subset\mathbb{R}^n$ satisfies $\mathrm{vol}(K+L)^{1/n}\geq\mathrm{vol}(K)^{1/n}+\mathrm{vol}(L)^{1/n}$. In this paper we obtain two discrete analogs of it for the cardinality of finite subsets of the integer lattice ${\mathbb{Z}}^n$.
María A. Hernández Cifre, David Iglesias, Jesús Yepes Nicolás   +2 more
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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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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
openaire   +3 more sources

Hölder’s Inequality, Minkowski’s Inequality and Their Variants

2012
In 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.
openaire   +1 more source

Inequalities of Minkowski type

Real analysis exchange, 1994
Let f be a real nonnegative, nondecreasing function defined on segment a, b, and x_i are nonnegative nondecreasing functions with continuous first derivative. If p>1, then (\int_a^b (\sum_{; ; i=1}; ; ^n x_i^p(t))'f(t)dt)^{; ; 1/p}; ; \geq \sum_{; ; i=1}; ; ^n (\int_a^b (x_i^p(t))'f(t)dt)^{; ; 1/p}; ; .
openaire   +1 more source

Dar’s conjecture and the log–Brunn–Minkowski inequality

, 2016
Dong-Meng Xi, G. Leng
semanticscholar   +1 more source

More Generalizations of Hartfiel’s Inequality and the Brunn–Minkowski Inequality

, 2020
S. Dong, Qingwen Wang
semanticscholar   +1 more source