A note on three-parameter families and generalized convex functions
type: Item
instance of: scholarly article
title: A note on three-parameter families and generalized convex functions
zbMATH Open document ID: 1126.26012
author: Mirosław Adamek
author: Attila Gilányi
author: Zsolt Páles
author: Kazimierz Nikodem
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-05-04T00:00:00Z
review text: Using a three-parameter family , the authors extend the idea by \textit{E. F. Beckenbach} [Bull. Am. Math. Soc. 43, 363--371 (1937; Zbl 0016.35202)] to two-variable functions and introduce \({\mathcal F}\)-convex, \({\mathcal F}\)-midconvex and \(({\mathcal F}, M)\)-convex functions, and prove some of their properties. It is noteworthy that \({\mathcal F}\)-convex functions defined on convex sets are continuous on the interiors of these sets, and lower-semicontinuous \({\mathcal F}\)-midconvex and \(({\mathcal F}, M)\)-convex functions are also \({\mathcal F}\)-convex. Some illustrative examples are given as well.
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 26B05
zbMATH DE Number: 5149495
zbMATH Keywords: three-parameter families
zbMATH Keywords: generalized convex functions
zbMATH Keywords: \({\mathcal F}\)-convex functions
zbMATH Keywords: \({\mathcal F}\)-midconvex functions
zbMATH Keywords: \(({\mathcal F},M)\)-convex functions
reviewed by: Do Van Luu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.07.067
OpenAlex ID: W1992827319
cites work: Generalized convex functions
cites work: On Generalized Convex Functions
cites work: Hadamard-type inequalities for generalized convex functions
cites work: Q5296430
cites work: Another Proof that Convex Functions are Locally Lipschitz
DOI: 10.1016/J.JMAA.2006.07.067
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description: scientific article; zbMATH DE number 5149495