A general Minkowski-type inequality for two variable Gini means
type: Item
instance of: scholarly article
zbMATH Open document ID: 0963.26009
author: P. Czinder
author: Zsolt Páles
publication date: 2001-04-01T00:00:00Z
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 1583121
zbMATH Keywords: Minkowski inequality
zbMATH Keywords: two variable homogeneous means
zbMATH Keywords: Gini means
MaRDI profile type: Publication
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title: A general Minkowski-type inequality for two variable Gini means
published in: Publicationes Mathematicae Debrecen
review text: The authors offer as ``main result'' necessary and sufficient conditions on \((a_0,b_0,a_1,b_1,a_2,b_2)\in\mathbb R^6\) for \(S_{a_0,b_0}(x+y)\leq S_{a_1,b_1}(x)+S_{a_2,b_2}(y)\) for all \((x,y)\in ]0,\infty[^4\) and the consequence that the inequality is `best' if \((a_0,b_0)=(a_1,b_1)=(a_2,b_2).\) Here \(S_{a,b}((u,v))\) is defined by \((\frac{u^a +v^a} {u^b+v^b})^{1/(b-a)}\) if \(a\neq b\) and by its limit as \(b\to a\) if \(a=b\). As (another) ``main result'' necessary and sufficient conditions for equality of such mean values are offered.
reviewed by: János Aczél
description: scientific article