Caratheodory’s Theorem for $\B^{-1}$-convex Sets
Authors :
G. Adilov a and I. Yesilce b,∗
Author Address :
a Department of Mathematics, Faculty of Education, Akdeniz University, Dumlupinar Boulevard 07058, Campus, Antalya, Turkey.
b Department of Mathematics, Faculty of Science and Letters, Mersin University, Ciftlikkoy Campus, 33343, Mersin, Turkey.
*Corresponding author.
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, $\mathbb B^{-1}-$convexity, $\mathbb B^{-1}-$convex sets, abstract convexity.
DOI :
Article Info :
Received : May 24, 2016; Accepted : July 17, 2016.