On the lower hull of convex functions
type: Item
instance of: scholarly article
title: On the lower hull of convex functions
zbMATH Open document ID: 0686.26003
DOI: 10.1007/BF01840005
author: Marek Kuczma
author: Zygfryd Kominek
published in: Aequationes Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137327
review text: In generalization of a result of \textit{F. Bernstein} and \textit{G. Doetsch} [Math. Ann. 76, 514-526 (1915)] the authors offer the following as main result. Let X be a real linear Baire space, D(\(\subset X)\) convex and open, and f:D\(\to [-\infty,\infty [\) midpoint-convex. Then \[ m_ f(x)=\sup_{U\in {\mathcal F}_ x}\inf_{t\in U\cap D}f(t) \] is continuous and convex. Here \({\mathcal F}_ x=\{U| x\in U\subset D\), U open\(\}\). Several related questions are discussed and a rich array of results is presented.
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 4124014
zbMATH Keywords: Baire topology
zbMATH Keywords: convex functions
zbMATH Keywords: continuous functions
zbMATH Keywords: lower hulls
zbMATH Keywords: real linear Baire space
zbMATH Keywords: midpoint-convex
MaRDI profile type: Publication
cites work: Q4159877
cites work: Q3785321
cites work: Q3218572
cites work: Q3708480
cites work: On Convex Functions
cites work: Q5338702
OpenAlex ID: W2001610365
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description: scientific article; zbMATH DE number 4124014