On Jessen's inequality for convex functions
type: Item
instance of: scholarly article
title: On Jessen's inequality for convex functions
zbMATH Open document ID: 0591.26009
DOI: 10.1016/0022-247X(85)90315-4
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: Let E be a nonempty set and let L be a linear space of real-valued functions on E; suppose that the constant function 1 belongs to L. Let \(\phi\) be a convex function on an interval \(I\subset R\) and let A be a positive linear functional on L, with \(A(1)=1.\) Then for all \(g\in L\) such that \(\phi (g)\in L\) we have \(A(g)\in I\) and \(\phi (A(g))\leq A(\phi (g))\) (Jessen's inequality). The authors give a short proof of this inequality and prove some general complementary inequalities. They obtain Hölder's and Minkowski's inequality for positive linear functionals, as well as certain complementary Hölder and Minkowski inequalities. Other known results are generalized and some examples and applications are given.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 3948642
zbMATH Keywords: generalization of Jensen's inequality for convex functions
zbMATH Keywords: Jessen's inequality
zbMATH Keywords: complementary Hölder and Minkowski inequalities
author: Paul R. Beesack
author: J. Pečarić
reviewed by: Ioan Raşa
MaRDI profile type: Publication
cites work: Q5682531
cites work: Q4081520
cites work: On Inequalities Complementary to Jensen's
cites work: Q3897234
cites work: Q4115339
cites work: The Generalization of Certain Inequality Theorems Involving Powers
cites work: Q5812325
cites work: Q3855396
cites work: Analytic Inequalities
full work available at URL: 0022-247x(85)90315-4
OpenAlex ID: W4205663189
description: scientific article; zbMATH DE number 3948642