A note on three-parameter families and generalized convex functions

Mirosław Adamek, Attila Gilányi, Kazimierz Nikodem, Zsolt Páles

Research output: Contribution to journalArticle

Abstract

The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363-371] is extended to the two-dimensional case. Using three-parameter families, we define generalized convex (midconvex, M-convex) functions f : D ⊆ R2 → R and show some continuity properties of them.

Original languageEnglish
Pages (from-to)829-835
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume330
Issue number2
DOIs
Publication statusPublished - Jun 15 2007

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Keywords

  • Generalized convex functions
  • Three-parameter families

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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