Optimal Lehmer mean bounds for the combinations of identric and logarithmic means
type: Item
instance of: scholarly article
title: Optimal Lehmer mean bounds for the combinations of identric and logarithmic means
zbMATH Open document ID: 1298.26097
DOI: 10.1155/2013/852516
author: Xu-Hui Shen
author: Wei-Ming Gong
author: Yu-Ming Chu
published in: Chinese Journal of Mathematics
publication date: 2014-10-16T00:00:00Z
review text: Summary: For any \(\alpha\in(0,1)\), we answer the questions: what are the greatest values \(p\) and \(\lambda\) and the least values \(q\) and \(\mu\), such that the inequalities \(L_p(a,b)< I^\alpha(a,b)L^{1-\alpha}(a,b)<L_q(a,b)\) and \(L_\lambda(a,b)<\alpha I(a,b)+(1-\alpha)L(a,b)<L_\mu(a,b)\) hold for all \(a,b>0\) with \(a\neq b\)? Here, \(I(a,b)\), \(L(a,b)\), and \(L_p(a,b)\) denote the identric, logarithmic, and \(p\)th Lehmer means of two positive numbers \(a\) and \(b\), respectively.
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 6356629
zbMATH Keywords: arithmetic-geometric mean
zbMATH Keywords: logarithmic mean
zbMATH Keywords: Gauss' hypergeometric function \(_2F_1\)
Wikidata QID: Q58920760
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/852516
OpenAlex ID: W1974907859
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description: scientific article; zbMATH DE number 6356629