A lower bound for ratio of power means
type: Item
instance of: scholarly article
title: A lower bound for ratio of power means
zbMATH Open document ID: 1065.26025
DOI: 10.1155/S0161171204208158
author: Feng Qi
author: Bai-Ni Guo
author: Lokenath Debnath
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51397
review text: Summary: Let \(n\) and \(m\) be natural numbers. Suppose that \(\{a_i\}_{i=1}^{n+m}\) is an increasing, logarithmically convex, and positive sequence. Denote the power mean \(P_n(r)\) for any given positive real number \(r\) by \(P_{n}(r)=((1/n)\sum_{i=1}^{n} a_i^r)^{1/r}\). Then \({P_n(r)}/{P_{n+m}(r)}\geq{a_n}/{a_{n+m}}\). The lower bound is the best possible.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 2168597
zbMATH Keywords: power means
zbMATH Keywords: Alzer inequality
zbMATH Keywords: Martin inequality
MaRDI profile type: Publication
OpenAlex ID: W1998984195
description: scientific article; zbMATH DE number 2168597