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 two-parameter family (in the sense of Beckenbach) is presented. As consequences, stability results of the Hyers-Ulam-type are also obtained.
|Number of pages||9|
|Journal||Journal of Convex Analysis|
|Publication status||Published - Jul 2 2007|
- Generalized convex functions
- Generalized convex sets
- Separation theorems
ASJC Scopus subject areas