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Convex separation by regular pairs

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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.

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Correspondence to Mihály Bessenyei.

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This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grants NK–81402 and by the TÁMOP 4.2.2.C-11/1/KONV-2012-0010 and TÁMOP 4.2.2/B-10/1-2010-0024 projects implemented through the New Hungary Development Plan co-financed by the European Social Fund, and the European Regional Development Fund.

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Bessenyei, M., Szokol, P. Convex separation by regular pairs. J. Geom. 104, 45–56 (2013).

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