Convexity with respect to families of means

Gyula Maksa, Z. Páles

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we investigate continuity properties of functions (Formula presented.) that satisfy the (p, q)-Jensen convexity inequality(Formula presented.)where Hp stands for the pth power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are (p, p)-Jensen convex for all positive rational numbers p. A counterpart of this result states that if f is (p, p)-Jensen convex for all (Formula presented.), where P is a set of positive Lebesgue measure, then f must be continuous.

Original languageEnglish
Pages (from-to)161-167
Number of pages7
JournalAequationes Mathematicae
Volume89
Issue number1
DOIs
Publication statusPublished - 2015

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Convexity
Multiplicative Functions
Discontinuous Functions
Lebesgue Measure
Family

Keywords

  • 26D15
  • Primary 39B62
  • Secondary 26D07

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Convexity with respect to families of means. / Maksa, Gyula; Páles, Z.

In: Aequationes Mathematicae, Vol. 89, No. 1, 2015, p. 161-167.

Research output: Contribution to journalArticle

Maksa, Gyula ; Páles, Z. / Convexity with respect to families of means. In: Aequationes Mathematicae. 2015 ; Vol. 89, No. 1. pp. 161-167.
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