
Journal of Convex Analysis 14 (2007), No. 2, 239247 Copyright Heldermann Verlag 2007 Generalized Convexity and Separation Theorems Kazimierz Nikodem Dept. of Mathematics, University of BielskoBiala, ul. Willowa 2, 43309 BielskoBiala, Poland knikodem@ath.bielsko.pl Zsolt Páles Institute of Mathematics, University of Debrecen, 4010 Debrecen Pf. 12, Hungary pales@math.klte.hu Kakutani's classical theorem (stating that two disjoint convex sets can be separated by complementary convex sets) is extended to the setting when convexity is meant in the sense of Beckenbach. Then a characterization of pairs of functions that can be separated by a generalized convex function or by a function belonging to a twoparameter family (in the sense of Beckenbach) is presented. As consequences, stability results of the HyersUlamtype are also obtained. Keywords: Generalized convex sets, generalized convex functions, separation theorems. MSC: 26A51, 52A01, 39B62 [ Fulltextpdf (116 KB)] for subscribers only. 