
Journal of Convex Analysis 20 (2013), No. 4, 937946 Copyright Heldermann Verlag 2013 Separation by Convex Interpolation Families Mihály Bessenyei Institute of Mathematics, University of Debrecen, Pf. 12, 4010 Debrecen, Hungary besse@science.unideb.hu Patrícia Szokol Institute of Mathematics, University of Debrecen, Pf. 12, 4010 Debrecen, Hungary szokolp@science.unideb.hu A set of continuous functions defined on an interval I is called an nparameter Beckenbach family, if each n points of I × R (with pairwise distinct first coordinates) can be interpolated by a unique element of the set. The aim of the present note is to characterize such pairs of real valued functions that can be separated by a member of a given convex Beckenbach family of order n. The key idea of the proof is to identify the family with R^{n} via a suitable homeomorphism. Then, the classical Helly Theorem guarantees the existence of a proper separator. Keywords: Interpolation families, Haar and Chebyshev systems, Separation theorems, Helly's Theorem. MSC: 26A51; 39B62, 52A20 [ Fulltextpdf (140 KB)] for subscribers only. 