Complementary inequalities involving the Stolarsky mean
type: Item
instance of: scholarly article
title: Complementary inequalities involving the Stolarsky mean
zbMATH Open document ID: 1208.26021
DOI: 10.1155/2010/492570
author: Ovidiu D. Bagdasar
published in: Journal of Inequalities and Applications
publication date: 2010-12-06T00:00:00Z
full work available at URL: https://eudml.org/doc/231623
review text: It is proved that the maximum of the function \[ f_{p,q}(a_1,\dots,a_n)=\frac{a_1^p+\dots+a_n^p}{n}-\left(\frac{a_1^q+\dots+a_n^q}{n}\right)^{p/q} \] (where \(p>q>0,\, b>a>0,\, a_1,\dots,a_n\in[a,b]\)) is attained if and only if \(k(n)\) of the numbers \(a_1,\dots,a_n\) are equal to \(a\) and the other \(n-k(n)\) are equal to \(b,\) while \(k(n)\) is one of the values \[ \left[n\frac{b^q-D^q_{p,q}(a,b)}{b^q-a^q}\right],\,\,\left[n\frac{b^q-D^q_{p,q}(a,b)}{b^q-a^q}\right]+1. \] Here \(D_{p,q}(a,b)\) is the Stolarsky mean of \(a\) and \(b\) of powers \(p\) and \(q.\) Also some asymptotic results for \(k(n)\) are given.
reviewed by: László Losonczi
Mathematics Subject Classification ID: 26D07
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5823175
zbMATH Keywords: Stolarsky mean
zbMATH Keywords: complementary inequality
Wikidata QID: Q59253923
MaRDI profile type: Publication
OpenAlex ID: W2129500441
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description: scientific article; zbMATH DE number 5823175