Radon’s and helly’s theorems for B−1 −convex sets

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KEMALİ S., Yesilce I., ADİLOV G.

Filomat, vol.35, no.3, pp.731-735, 2021 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 35 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2103731k
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.731-735
  • Keywords: Abstract convexity, B−1-convex sets, Caratheodory’s theorem, Helly’s theorem, Radon’s theorem
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

Helly’s, Radon’s, and Caratheodory’s theorems are the basic theorems of convex analysis and have an important place. These theorems have been studied by different authors for different classes of convexity. Caratheodory’s theorem for B−1 −convex sets has been proved before by Adilov and Yeşilce. In this article, Helly’s and Radon’s theorems are discussed and examined for these sets.