The starshapedness number and a Krasnosel'skij-type theorem in a convexity space
type: Item
instance of: scholarly article
title: The starshapedness number and a Krasnosel'skij-type theorem in a convexity space
zbMATH Open document ID: 0636.52002
DOI: 10.1007/BF01194302
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: In the context of a convexity space an analogue of Krasnoselskij's theorem on compact star sets in \({\mathbb{R}}^ n\) is given. The concept of starshapedness number is introduced and its relations with Carathéodory, Helly, Radon and exchange numbers are investigated.
Mathematics Subject Classification ID: 52A01
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 4036601
zbMATH Keywords: convexity space
zbMATH Keywords: Krasnoselskij's theorem
zbMATH Keywords: starshapedness number
author: Krzysztof Kołodziejczyk
reviewed by: Peter M. Gruber
MaRDI profile type: Publication
cites work: A Proof of the Equivalence of Helly's and Krasnoselski's Theorems
cites work: A Krasnosel'skii-Type Theorem for Points of Local Nonconvexity
cites work: A Characterization Theorem for Bounded Starshaped Sets in the Plane
cites work: Q5341481
cites work: Beziehungen zwischen den Sätzen von Radon, Helly und Caratheodory bei axiomatischen Konvexitäten
cites work: Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers
cites work: A refinement of Valentine's theorem
cites work: Q3709409
cites work: On starshapedness of the union of closed sets in $R^n$
cites work: Q5837707
cites work: Q5807392
cites work: Q4081945
cites work: Q4125422
cites work: Q3902107
cites work: Q3851227
cites work: Q5185609
cites work: Krasnosel'skii Theorems for Non-Separating Compact Sets
cites work: Q5338702
full work available at URL: https://doi.org/10.1007/bf01194302
OpenAlex ID: W2028519561
description: scientific article; zbMATH DE number 4036601