Hölder-type inequalities for quasiarithmetic means
type: Item
instance of: scholarly article
title: Hölder-type inequalities for quasiarithmetic means
zbMATH Open document ID: 0605.26020
DOI: 10.1007/BF01953978
author: Zsolt Páles
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: In generalization of a theorem of \textit{L. Losonczi} [General inequalities 3, 3rd int. Conf., Oberwolfach 1981, ISNM 64, 91-106 (1983; Zbl 0573.26011)], and in a more elementary manner, the following is proved: \[ \frac{1}{n}\sum^{n}_{i=1}\prod^{k}_{j=1}x_{ij} \leq \prod^{k}_{j=1}\phi_ j^{-1}(\frac{1}{n}\sum^{n}_{i=1}\phi_ j(x_{ij}))\quad (x>0;\quad n=1,2,...) \] iff there exist \(p_ j>1\) \((j=1,...,k)\) with \(\sum^{k}_{j=1}(1/p_ j)=1\) such that \[ (\frac{1}{n}\sum^{n}_{i=1}x_ i^{p_ j})^{1/p_ j} \leq \phi_ j^{-1}(\frac{1}{n}\sum^{n}_{i=1}\phi_ j(x_ i))\quad (x_ i>0;\quad j=1,2,...,k;\quad n=1,2,...). \]
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 3977324
zbMATH Keywords: continuous strictly monotonic functions
zbMATH Keywords: convex functions
zbMATH Keywords: quasiarithmetic means
zbMATH Keywords: Hölder-type inequalities
MaRDI profile type: Publication
cites work: Q3691970
description: scientific article; zbMATH DE number 3977324