Caratheodory's theorem for $\mathbb{B}^{-1}$-convex sets

G. Adilov; I. Yesilce

doi:10.26637/mjm403/013

Abstract

In this article, our main concept is $\mathbb{B}^{-1}$-convexity that is a new abstract convexity type. For the $\mathbb{B}^{-1}$-convex sets, Caratheodory's Theorem which is one of the most important results in convexity theory is proved and its corollary is given.

Keywords:

Caratheodory’s Theorem, abstract convexity, $B^{ − 1}$ − convexity , $B ^{− 1}$ − convex sets

Mathematics Subject Classification:

52A20, 52A35, 52A05

Authors Imprint References Funding Related Articles Downloads

G. Adilov Department of Mathematics, Faculty of Education, Akdeniz University, Dumlupinar Boulevard 07058, Campus, Antalya, Turkey.
I. Yesilce Department of Mathematics, Faculty of Science and Letters, Mersin University, Ciftlikkoy Campus, 33343, Mersin, Turkey.

Pages: 444-447
Date Published: 01-07-2016
Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

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