Some Jessen-Beckenbach inequalities
type: Item
instance of: scholarly article
title: Some Jessen-Beckenbach inequalities
zbMATH Open document ID: 0652.26024
DOI: 10.1216/RMJ-1987-17-3-629
author: J. Pečarić
author: Paul R. Beesack
published in: Rocky Mountain Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: One of the main results offered is the following. Let E be a nonempty set, \({\mathcal A}\) an algebra of its subsets and L a linear class of functions \(f: E\to {\mathbb{R}}\) containing the constant function and the characteristic functions of elements of \({\mathcal A}\). Furthermore, let B be a linear functional on L satisfying \(B(1)=1\) and \(B(f)\geq 0\) if \(f\geq 0\), I a closed real interval, \(\phi: I\to J\) convex, \(F: J^ 2\to {\mathbb{R}}\) nondecreasing in its first variable and \(F^ 2(x)=F(x,x).\) If \(E_ 1\in {\mathcal A}\) is such that B is positive on the characteristic function of \(E\setminus E_ 1\), then, for any \(g\in L\) with \(\phi(g)\in L\), \[ F^ 2(B[\phi(g)])\geq \inf_{x\in I}F^ 2(B[\phi(gC_ 1+xC_ 2)]), \] where \(C_ 1\) and \(C_ 2\) are the characteristic functions of \(E_ 1\) and \(E\setminus E_ 1\), respectively. \{In line 2 of p. 633, the third m should be M.\}
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 47B60
zbMATH DE Number: 4063445
zbMATH Keywords: isotonic linear functionals
zbMATH Keywords: Jessen-Beckenbach inequality
zbMATH Keywords: McShane's inequality
zbMATH Keywords: characteristic functions
MaRDI profile type: Publication
full work available at URL: rmj-1987-17-3-629
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description: scientific article; zbMATH DE number 4063445