On Jensen's inequality for a class of functions of Godunova and Levin
type: Item
instance of: scholarly article
title: On Jensen's inequality for a class of functions of Godunova and Levin
zbMATH Open document ID: 0880.26011
DOI: 10.1007/BF02093506
published in: Periodica Mathematica Hungarica
publication date: 1998-01-07T00:00:00Z
review text: The authors investigate inequalities for functions \(f:C\to\hbox{\mathbf R}\) satisfying \[ f(\lambda x+(1-\lambda)y)\leq {f(x)\over \lambda}+{f(y)\over1-\lambda} \] for all \(x,y\in C\) and \(\lambda\in(0,1)\) (where \(C\) denotes a convex set of a real linear space). These functions are said to belong to the class \(Q\) by the terminology of \textit{E.K. Godunova} and \textit{V.I. Levin} [``Inequalities for functions of a broad class that contains convex monotone and some other forms of functions'' (Russian), Numer. Math. and Math. Phys. 138-142, 166 (1985; MR 88h:26013)]. The main results of the paper offer inequalities for the comparison of expressions of the following form \[ \sum_{i_1,\dots,i_k=1}^n {f(q_1x_{i_1}+\cdots+q_kx_{i_k}) \over p_{i_1}\cdots p_{i_k}}, \] where \(\bar{p}=(p_1,\dots,p_n)\) is a positive probability distribution, \(\bar{q}=(q_1,\dots,q_k)\) is a nonnegative probability distribution and \(x_1,\dots,x_n\in C\).
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 1101397
zbMATH Keywords: Jensen's inequality
zbMATH Keywords: functions of class \(Q\)
author: Silvestru Sever Dragomir
author: Charles E. M. Pearce
reviewed by: Zsolt Páles
MaRDI profile type: Publication
cites work: Q3478646
cites work: Q5287501
cites work: Q4205660
cites work: Schur’s Inequality
cites work: 2627. A generalisation of Schur's inequality
full work available at URL: https://doi.org/10.1007/bf02093506
OpenAlex ID: W1989065036
description: scientific article; zbMATH DE number 1101397