Bernstein-Doetsch type results for quasiconvex functions

Attila Gilányi, Kazimierz Nikodem, Zsolt Páles

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume7
Issue number2
DOIs
Publication statusPublished - Apr 2004

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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