On functional equations involving means

Zoltán Daróczy, Z. Páles

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The main results of the paper concern functional equations of the form f(M(x,y))(g(y) - g(x)) = μ(f(x)g(y) - f(y)g(x)) (x, y ∈ I), where f and g are continuous functions defined on an open interval I and M is a strict two variable mean on I. As an application, a generalization of the so-called Matkowski-Sutô problem for weighted two variable quasi-arithmetic means is solved under first-order continuous differentiability assumptions.

Original languageEnglish
Pages (from-to)363-377
Number of pages15
JournalPublicationes Mathematicae
Volume62
Issue number3-4
Publication statusPublished - 2003

Fingerprint

Functional equation
Quasi-arithmetic Mean
Open interval
Differentiability
Continuous Function
First-order
Generalization
Form

Keywords

  • Functional equation
  • Matkowski-Sutô problem
  • Stolarsky means
  • Weighted quasi-arithmetic mean

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On functional equations involving means. / Daróczy, Zoltán; Páles, Z.

In: Publicationes Mathematicae, Vol. 62, No. 3-4, 2003, p. 363-377.

Research output: Contribution to journalArticle

Daróczy, Z & Páles, Z 2003, 'On functional equations involving means', Publicationes Mathematicae, vol. 62, no. 3-4, pp. 363-377.
Daróczy, Zoltán ; Páles, Z. / On functional equations involving means. In: Publicationes Mathematicae. 2003 ; Vol. 62, No. 3-4. pp. 363-377.
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