Characterizations of higher-order convexity properties with respect to Chebyshev systems
type: Item
instance of: scholarly article
title: Characterizations of higher-order convexity properties with respect to Chebyshev systems
zbMATH Open document ID: 1351.26026
author: Zsolt Páles
author: Éva Székelyné Radácsi
published in: Aequationes Mathematicae
publication date: 2016-04-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1505.00617
review text: Using the general Chebyshev systems \(\omega \) the authors introduce various notions of convexity of real functions (\(\omega \) -convexity, \(\left( t,\omega \right) \)-convexity, \(\omega \)-Jensen convexity) and extend some standard convexity results presented in [\textit{A. Gilańyi} and \textit{Z. Páles}, Math. Inequal. Appl. 11, No. 2, 271--282 (2008; Zbl 1141.26304)] and [\textit{K. Nikodem} and \textit{Z. Páles}, Real Anal. Exch. 29, No. 1, 219--228 (2004; Zbl 1076.26008)]. They obtain various characterizations of convexity properties in terms of the nonnegativity of a generalized divided difference and the corresponding lower Dinghas type derivative. Among others, they show that these convexity properties are localizable.
reviewed by: Małgorzata Wróbel
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 39B62
zbMATH DE Number: 6563693
zbMATH Keywords: Chebyshev system
zbMATH Keywords: generalized convexity
zbMATH Keywords: generalized divided difference
zbMATH Keywords: generalized lower Dinghas type derivative
MaRDI profile type: Publication
OpenAlex ID: W1789875020
arXiv ID: 1505.00617
cites work: Q3808598
cites work: Q5519280
cites work: On convex functions of higher order
cites work: Q5624248
cites work: Q5534404
cites work: Q3218572
cites work: Q3710945
cites work: On \(t\)-convex functions
cites work: Q5835310
DOI: 10.1007/S00010-015-0377-8
description: scientific article; zbMATH DE number 6563693