The Kantorovich inequality under integral constraints
type: Item
instance of: scholarly article
title: The Kantorovich inequality under integral constraints
zbMATH Open document ID: 0805.26013
author: L. Migíaccio
author: Luciana Nania
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-06-16T00:00:00Z
review text: Let \(f: [0,1]\to [m,M]\), where \(0< m< M<\infty\). If, in addition, \(\int^ 1_ 0 f^{-1}(x)dx\leq m^{-1}\), we write \(f\in A^ 1_{m,M}\). The authors proved that for any \(f\in A^ 1_{m,M}\), \[ \int^ 1_ 0 f^ 2(x)dx\leq (4m)^{-1}[M- N+ (M+ m)^ 2/M]\left(\int^ 1_ 0 f(x)dx\right)^ 2 \] and that the equality sign occurs iff the non-increasing rearrangement \(f^*\) of \(f\) is given by \(f^*(t)= M\) for \(t\in [0,m/M)\) and \(f^*(t)= mM/(m+ M)\) for \(t\in [m/M,1]\).
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 566992
zbMATH Keywords: Kantorovich inequality
zbMATH Keywords: integral constraints
zbMATH Keywords: rearrangement
reviewed by: Bohumír Opic
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1041
OpenAlex ID: W1994499200
DOI: 10.1006/JMAA.1994.1041
description: scientific article; zbMATH DE number 566992