Journal of Geometry

, Volume 104, Issue 1, pp 45–56 | Cite as

Convex separation by regular pairs

  • Mihály BessenyeiEmail author
  • Patrícia Szokol


It is known that the existence of a convex (resp., concave) separator between two given functions can be characterized via a simple inequality. The notion of convexity can be generalized applying regular pairs (in other words, two dimensional Chebyshev systems). The aim of the present note is to extend the above mentioned result to this setting. In the proof, a modified version of the classical Carathéodory’s theorem and the characterization of convex functions play the key role.

Mathematics Subject Classification (2010)

26A51 39B62 52A20 


Convexity Chebyshev systems separation theorems Carathéodory’s theorem 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary

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