Some counterpart inequalities for a functional associated with Jensen's inequality
type: Item
instance of: scholarly article
title: Some counterpart inequalities for a functional associated with Jensen's inequality
zbMATH Open document ID: 0886.26010
DOI: 10.1155/S1025583497000210
author: C. J. Goh
author: Silvestru Sever Dragomir
published in: Journal of Inequalities and Applications
publication date: 1998-02-26T00:00:00Z
full work available at URL: https://eudml.org/doc/119314
review text: The authors offer properties of \[ \sum_{i\in I} p_if({\mathbf x}_i)-P_If(\sum_{i\in I}p_i{\mathbf x}_i/P_I). \] Here \(f\) is supposed to be a convex (and most of the time differentiable) real valued function on a convex subset \(C\) of a (mostly finite dimensional) linear space, \({\mathbf x}_i\in C\), the \(p_i\) are positive reals, \(i\in I\), \(I\) is a finite set of positive integers and \(P_I=\sum_{i\in I} p_i\) (though the last equation seems to have been omitted from the paper or thought to go without saying). Applications to arithmetic and geometric means and to the Shannon inequality are offered.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1086031
zbMATH Keywords: convex functions
zbMATH Keywords: Jensen inequality
zbMATH Keywords: Shannon inequality
zbMATH Keywords: arithmetic and geometric means
reviewed by: János Aczél
MaRDI profile type: Publication
OpenAlex ID: W2047642783
description: scientific article; zbMATH DE number 1086031