Sharp bounds for power mean in terms of generalized Heronian mean
type: Item
instance of: scholarly article
title: Sharp bounds for power mean in terms of generalized Heronian mean
zbMATH Open document ID: 1218.26022
DOI: 10.1155/2011/679201
author: Hongya Gao
author: Jianling Guo
author: Wanguo Yu
published in: Abstract and Applied Analysis
publication date: 2011-07-22T00:00:00Z
review text: Summary: For \(1 < r < +\infty\), we find the least value \(\alpha\) and the greatest value \(\beta\) such that the inequality \(H_{\alpha}(a, b) < A_r(a, b) < H_{\beta}(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\). Here, \(H_{\omega}(a, b)\) and \(A_r(a, b)\) are the generalized Heronian and the power means of two positive numbers \(a\) and \(b\), respectively.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5930770
zbMATH Keywords: power mean
zbMATH Keywords: Heronian mean
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/679201
OpenAlex ID: W2156788334
Wikidata QID: Q58654396
cites work: A note on generalized Heronian means
cites work: Two sharp inequalities for power mean, geometric mean, and harmonic mean
cites work: Optimal power mean bounds for the weighted geometric mean of classical means
cites work: Optimal inequalities among various means of two arguments
cites work: The generalized Heronian mean and its inequalities
cites work: Q4412336
cites work: The optimization for the inequalities of power means
cites work: Q4464282
cites work: Best possible inequalities between generalized logarithmic mean and classical means
cites work: Inequalities for generalized logarithmic means
cites work: The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means
cites work: A refinement of various mean inequalities
cites work: On certain means of two arguments and their extensions
description: scientific article; zbMATH DE number 5930770