A converse of Minkowski's type inequalities
type: Item
instance of: scholarly article
title: A converse of Minkowski's type inequalities
zbMATH Open document ID: 1208.26040
DOI: 10.1155/2010/461215
author: Romeo Meštrović
author: David Kalaj
published in: Journal of Inequalities and Applications
publication date: 2010-12-06T00:00:00Z
review text: Let \(p>0, q>0,\) and \(a_{ij}\geq 0\, (i=1,\dots,m;j=1,\dots,n)\) be real numbers. Then for \(p\geq 1\) the (converse Minkowski) inequality \[ \sum_{i=1}^m\left(\sum_{j=1}^n a_{ij}^p\right)^{1/p}\leq C\left(\sum_{j=1}^n\left(\sum_{i=1}^m a_{ij}^q\right)^{p/q}\right)^{1/p} \] holds, where \(C=C(m,n,p,q)\) is a positive constant whose dependence on its parameters is given. For \(0< p<1\) the inequality sign is reversed (and another constant is needed). Analogous integral inequalities are also obtained.
reviewed by: László Losonczi
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 5823171
zbMATH Keywords: Minkowski's inequality
zbMATH Keywords: converse inequality
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/461215
OpenAlex ID: W1995426072
Wikidata QID: Q59252825
cites work: Q5817530
cites work: Q4039929
cites work: Q3276750
cites work: On the inequality of Ingham and Jessen
cites work: A converse of Minkowski's inequality
description: scientific article; zbMATH DE number 5823171