Sharp power mean bounds for the combination of Seiffert and geometric means
type: Item
instance of: scholarly article
title: Sharp power mean bounds for the combination of Seiffert and geometric means
zbMATH Open document ID: 1197.26054
DOI: 10.1155/2010/108920
author: Yu-Ming Chu
author: Yefang Qiu
author: Miao-Kun Wang
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/224018
review text: Summary: We answer the question: for \(\alpha \in (0,1)\), what are the greatest value \(p\) and the least value \(q\) such that the double inequality \(M_{p}(a,b)<P^\alpha(a,b)G^{1-\alpha}(a,b)<M_q(a,b)\) holds for all \(a,b>0\) with \(a\neq b\). Here, \(M_{p}(a,b)\), \(P(a,b)\), and \(G(a,b)\) denote the power of order \(p\), Seiffert, and geometric means of two positive numbers \(a\) and \(b\), respectively.
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5791602
Wikidata QID: Q58649720
MaRDI profile type: Publication
OpenAlex ID: W2055195720
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description: scientific article; zbMATH DE number 5791602