A best possible double inequality for power mean
type: Item
instance of: scholarly article
title: A best possible double inequality for power mean
zbMATH Open document ID: 1316.26035
DOI: 10.1155/2012/379785
author: Bo-Yong Long
author: Yu-Ming Chu
author: Yongmin Li
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: We answer the question: for any \(p, q \in \mathbb R\) with \(p \neq q\) and \(p \neq -q\), what are the greatest value \(\lambda = \lambda(p, q)\) and the least value \(\mu = \mu(p, q)\), such that the double inequality \(M_\lambda(a, b) < \sqrt{M_p(a, b) M_q(a, b)} < M_\mu(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\)? Where \(M_p(a, b)\) is the \(p\)th power mean of two positive numbers \(a\) and \(b\).
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 6169895
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/379785
OpenAlex ID: W2000471620
Wikidata QID: Q58906775
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description: scientific article; zbMATH DE number 6169895