On nonconvexity of graphs of polynomials of several real variables
type: Item
instance of: scholarly article
title: On nonconvexity of graphs of polynomials of several real variables
zbMATH Open document ID: 0916.54013
DOI: 10.1023/A:1008655707873
author: Pavel V. Semenov
author: Dušan Repovš
published in: Set-Valued Analysis
publication date: 1999-07-19T00:00:00Z
review text: To every nonempty closed subset of a Banach space a measure of nonconvexity is associated. It is proved, that a suitable estimate of nonconvexity of graphs of continuous functions over all lines induces a nice estimate of the nonconvexity of graphs of the entire functions. Such result implies the existence of continuous selections for multifunctions the values of which are graphs of the considered functions. Positive results for quadratic forms and negative ones for cubics are provided. The proofs are geometrical in nature and the paper contains 9 pictures.
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 52A21
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 1230457
zbMATH Keywords: functions of nonconvexity
zbMATH Keywords: functional paraconvexity
zbMATH Keywords: graph of function
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
full work available at URL: a:1008655707873
OpenAlex ID: W143956444
description: scientific article; zbMATH DE number 1230457