On the inequalities of Ky Fan, Wang-Wang and Alzer
type: Item
instance of: scholarly article
title: On the inequalities of Ky Fan, Wang-Wang and Alzer
zbMATH Open document ID: 1012.26019
DOI: 10.1016/S0022-247X(02)00074-4
author: Vidan Govedarica
author: Milan V. Jovanović
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-09-08T00:00:00Z
review text: Let \(A\), \(G\) and \(H\) (or \(A(a)\), \(G(a)\) and \(H(a)\)) be, respectively, the unweighted arithmetic, geometric and harmonic means of the real numbers \(a_1,\dots, a_n\) (\(a_i>0\), \(i= 1,\dots, n\)). Let \(1= (1,\dots, 1)\) and \(A^+= A(1+ a)\), \(G^+= G(1+a)\), \(H^+= H(1+ a)\), then \[ {1\over H^+}- {1\over H}\leq {1\over G^+}- {1\over G}\leq {1\over A^+}- {1\over A} \] with equalities iff \(a_1=\cdots= a_n\). New proofs of Ky Fan, Wang-Wang, Alzer and El-Neweihi-Proschan inequalities are also given.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 1797532
zbMATH Keywords: Ky Fan inequality
zbMATH Keywords: arithmetic mean
zbMATH Keywords: geometric mean
zbMATH Keywords: harmonic mean
reviewed by: J. Pečarić
MaRDI profile type: Publication
cites work: Inequalities for Arithmetic, Geometric and Harmonic Means
cites work: Unified Treatment of Some Inequalities Among Ratios of Means
full work available at URL: s0022-247x(02)00074-4
OpenAlex ID: W2018097575
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description: scientific article; zbMATH DE number 1797532