Sets of convexity of continuous functions
type: Item
instance of: scholarly article
title: Sets of convexity of continuous functions
zbMATH Open document ID: 0668.26008
DOI: 10.1007/BF01951574
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: The purpose of this paper is to show that, for a continuous function \(f: {\mathbb{R}}\to {\mathbb{R}}\) at least one of the following holds; there is a real interval on which f is convex (or concave) or there exist two non empty perfect subsets H, K of \({\mathbb{R}}\) such that the restriction of f to H or K are strictly convex or strictly concave, respectively.
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 4093809
zbMATH Keywords: perfect sets
zbMATH Keywords: continuous convex functions
zbMATH Keywords: second category set
zbMATH Keywords: residual
zbMATH Keywords: everywhere dense set
zbMATH Keywords: first category set
author: Zoltán Buczolich
MaRDI profile type: Publication
cites work: Convexity Conditions and Intersections with Smooth Functions
cites work: Sur les fonctions continues relativement monotones
full work available at URL: https://doi.org/10.1007/bf01951574
OpenAlex ID: W2093419485
description: scientific article; zbMATH DE number 4093809