A characterization of midpoint-quasiaffine functions

Kazimierz Nikodem, Z. Páles

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider the functional inequality (equation presented) where f is a real valued function on a linear space X. This inequality is satisfied by Jensen functions (that are solutions of the Jensen functional equation) and, in the case X = ℝ, by monotone functions. The main result of the paper shows that, under some regularity assumptions, any solution of (*) is of the form f = g o α, where α : X → ℝ is an additive function and g : ℝ → ℝ is monotone.

Original languageEnglish
Pages (from-to)575-595
Number of pages21
JournalPublicationes Mathematicae
Volume52
Issue number3-4
Publication statusPublished - 1998

Fingerprint

Midpoint
Jensen Functional Equation
Functional Inequalities
Additive Function
Monotone Function
Linear Space
Monotone
Regularity
Form

Keywords

  • ℚ-quasiaffine function
  • Jensen function
  • Midpoint-convex and ℚ-convex set
  • Midpoint-quasiaffine function

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A characterization of midpoint-quasiaffine functions. / Nikodem, Kazimierz; Páles, Z.

In: Publicationes Mathematicae, Vol. 52, No. 3-4, 1998, p. 575-595.

Research output: Contribution to journalArticle

Nikodem, Kazimierz ; Páles, Z. / A characterization of midpoint-quasiaffine functions. In: Publicationes Mathematicae. 1998 ; Vol. 52, No. 3-4. pp. 575-595.
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