Inequalities for elementary means.
type: Item
instance of: scholarly article
title: Inequalities for elementary means.
zbMATH Open document ID: 0813.26009
DOI: 10.1007/BF01196631
author: Heinz-Jürgen Seiffert
published in: Archiv der Mathematik
publication date: 1995-05-29T00:00:00Z
review text: Für die verschiedenen positiven Zahlen \(x\) und \(y\) seien \(G(x, y):= \sqrt{xy}\), \(A(x, y):= (x+ y)/2\), \(L(x, y):= (x- y)/(\ln x- \ln y)\) und \(I(x, y):= e^{-1}(x^ x/ y^ y)^{1/(x- y)}\). Gezeigt werden die Ungleichungen \[ L(x, y)< \sqrt{L(G(x, y)^ 2, A(x,y)^ 2)}< \sqrt{I(G(x, y)^ 2, A(x, y)^ 2)}< I(x, y). \] Die rechte Seite dieser Ungleichungskette sowie einige weitere Ungleichungen, werden unter Benutzung von Identitäten bewiesen.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 734505
zbMATH Keywords: inequalities
zbMATH Keywords: means
MaRDI profile type: Publication
cites work: Extended Mean Values
cites work: Extended mean values. II
cites work: On the identric and logarithmic means
cites work: Generalizations of the Logarithmic Mean
full work available at URL: https://doi.org/10.1007/bf01196631
OpenAlex ID: W2063470584
description: scientific article; zbMATH DE number 734505