\(s\)-Orlicz convex functions in linear spaces and Jensen's discrete inequality
type: Item
instance of: scholarly article
title: \(s\)-Orlicz convex functions in linear spaces and Jensen's discrete inequality
zbMATH Open document ID: 0888.46005
author: Silvestru Sever Dragomir
author: Simon Fitzpatrick
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-05-21T00:00:00Z
review text: The authors generalize apparently unpublished results of H. Hudzik and L. Maligranda (Preprint 02-1992, LuleåUniv. of Technology, Sweden) from the reals to linear spaces. They call a subset \(K\) of a linear space ``\(s\)-Orlicz-convex'' if, with every \(x\) and \(y\) in \(K\) also \(\alpha x+\beta y\in K\) for all nonnegative \(\alpha,\beta\) satisfying \(\alpha^{s}+\beta^{s} = 1\). A real valued mapping on \(K\) is \(s\)-Orlicz-convex if for all such \(x,y,\alpha,\beta\) we have \(f(\alpha x + \beta y) \leq \alpha^{s}f(x) + \beta^{s}f(y)\). The authors offer, among others, several generalizations of this Jensen inequality.
reviewed by: János Aczél
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 1046937
zbMATH Keywords: Jensen inequality
zbMATH Keywords: generalized convexity
zbMATH Keywords: linear space
zbMATH Keywords: Orlicz convex
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5385
OpenAlex ID: W1995913247
DOI: 10.1006/JMAA.1997.5385
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description: scientific article; zbMATH DE number 1046937