Bernstein-Doetsch type results for quasiconvex functions

Attila Gilányi, Kazimierz Nikodem, Zsolt Páles

Research output: Contribution to journalArticle

9 Citations (Scopus)


In this paper various quasiconvexity notions are considered and compared. The main goal is to show that, under the assumption of upper semicontinuity, Jensen-type quasiconvexity properties are equivalent to the corresponding ordinary quasiconvexity property. The results thus obtained are analogous to the classical theorem of Bernstein and Doetsch for convex functions. Finally, the connection between approximate Jensen quasiconvexity and approximate quasiconvexity is investigated.

Original languageEnglish
Pages (from-to)169-175
Number of pages7
JournalMathematical Inequalities and Applications
Issue number2
Publication statusPublished - Apr 2004


  • Jensen-quasiconvex function
  • Quasiconvex function
  • Upper semicontinuity
  • ε-Jensen-quasiconvex function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Bernstein-Doetsch type results for quasiconvex functions'. Together they form a unique fingerprint.

  • Cite this