On a generalization of Mulholland's inequality
type: Item
instance of: scholarly article
title: On a generalization of Mulholland's inequality
zbMATH Open document ID: 0791.26014
DOI: 10.1007/BF02941335
author: Janusz Matkowski
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1994-02-06T00:00:00Z
review text: The author offers as main result the following. Let \(g\) be a convex homeomorphism of the nonnegative reals, such that also \(\log\circ g\circ\exp\) be convex. Then for all nonnegative \(x_ k\), \(y_ k\) and for all \(a_ k\) not smaller than 1 \((k=1,\dots,n)\), \[ g^{- 1}\left(\sum^ n_{k=1} a_ k g(x_ h+ y_ k)\right)\leq g^{- 1}\left(\sum^ n_{k=1} a_ k g(x_ k)\right)+ g^{-1}\left(\sum^ n_{k=1} a_ k g(y_ k)\right). \] As a consequence, in a result of the author in Proc. Am. Math. Soc. 190, No. 3, 663-675 (1990; Zbl 0704.46020) the following requirement cannot be dropped: there exists a set of measure strictly between 0 and 1 in the measure space there defined.
reviewed by: János Aczél
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 492586
zbMATH Keywords: Minkowski inequality
zbMATH Keywords: Mulholland inequality
zbMATH Keywords: convex functions
MaRDI profile type: Publication
cites work: Q3218572
cites work: The Converse of the Minkowski's Inequality Theorem and its Generalization
cites work: On Generalizations of Minkowski's Inequality in the Form of a Triangle Inequality
full work available at URL: https://doi.org/10.1007/bf02941335
OpenAlex ID: W2051112327
description: scientific article; zbMATH DE number 492586