Results 181 to 190 of about 1,075 (214)

Minkowski–Bellman inequality and equation

Automatica, 2021
The paper offers characterizations for the Minkowski-Bellman functions and the corresponding optimal set-valued control maps, with real possibilities of extensions to the parametric uncertain linear systems.
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THE ISOLATION FORM OF BRUNN-MINKOWSKI INEQUALITY AND MINKOWSKI INEQUALITY IN L_p SPACE

Far East Journal of Mathematical Sciences (FJMS), 2017
Summary: This article is devoted to the study of inequality form of segregation. First, we establish the isolate forms of the Brunn-Minkowski inequality for the dual \(p\)-quermassintegrals of the dual Firey linear combination. Then we give the isolate forms of the new dual \(L_p\)-Brunn-Minkowski inequality for dual quermassintegrals of the \(L_p ...
Xie, Fengfan, Yin, Qian
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On Reverse Minkowski-Type Inequalities

Mediterranean Journal of Mathematics, 2014
zbMATH 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

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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Brunn–Minkowski and Zhang inequalities for convolution bodies [PDF]

Advances in Mathematics, 2013
A quantitative version of Minkowski sum, extending the definition of θ-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties on Convex Geometry involving ...
Rafael Villa, C Hugo Jiménez, David Alonso-Gutiérrez   +2 more
exaly   +3 more sources

Stability of Inequalities in the Dual Brunn-Minkowski Theory [PDF]

Journal of Mathematical Analysis and Applications, 1999
Stability versions are given of several inequalities from E. Lutwak's dual Brunn-Minkowski theory. These include the dual Aleksandrov-Fenchel inequality, the dual Brunn-Minkowski inequality, and the dual isoperimetric inequality. Two methods are used.
Vassallo, Salvatore Flavio
exaly   +4 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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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
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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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