An inequality for arithmetic and harmonic means
type: Item
instance of: scholarly article
title: An inequality for arithmetic and harmonic means
zbMATH Open document ID: 0785.26012
author: Horst Alzer
published in: Aequationes Mathematicae
publication date: 1994-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/137558
review text: The following result is proved: If \(A_ n\) and \(H_ n\) (resp. \(A_ n'\) and \(H_ n')\) denote the arithmetic and harmonic means of \(x_ 1,\ldots,x_ n\) (resp. \(1-x_ 1,\ldots,1-x_ n)\) with \(x_ i\in(0,1/2]\) \((i=1,\ldots,n)\), then \[ H_ n-H_ n'\leq A_ n-A_ n', \] with equality if and only if \(x_ 1=\cdots=x_ n\).
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 493227
zbMATH Keywords: arithmetic mean
zbMATH Keywords: harmonic mean
zbMATH Keywords: inequality
reviewed by: J. Pečarić
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 493227