Generalized convexity and separation theorems

Kazimierz Nikodem, Zsolt Páles

Research output: Contribution to journalArticle

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)239-247
Number of pages9
JournalJournal of Convex Analysis
Issue number2
Publication statusPublished - Jul 2 2007


  • Generalized convex functions
  • Generalized convex sets
  • Separation theorems

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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