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Inequalities of Minkowski type
Real analysis exchange, 1994Let 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}; ; .
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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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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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Regular Black Holes with Asymptotically Minkowski Cores
Universe, 2020Alexander Marcus Simpson, Matt Visser
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Minkowski metric, feature weighting and anomalous cluster initializing in K-Means clustering
Pattern Recognition, 2012Renato Cordeiro de Amorim +1 more
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Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems
Acta Mathematica, 2016Yong Huang, Erwin Lutwak, Deane Yang
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Minkowski-type distance measures for generalized orthopair fuzzy sets
International Journal of Intelligent Systems, 2018Wen Sheng Du
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