Functional equations involving means

Z. Daróczy, K. Lajkó, R. L. Lovas, Gy Maksa, Zs Páles

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper, the functional equation f(px + (1 - p)y) + f((1 - p)x + py) = f(x) + f(y), (x,y \in I) is considered, where 0 < p < 1 is a fixed parameter and f: I → R is an unknown function. The equivalence of this and Jensen's functional equation is completely characterized in terms of the algebraic properties of the parameter p. As an application, solutions of certain functional equations involving four weighted arithmetic means are also determined.

Original languageEnglish
Pages (from-to)79-87
Number of pages9
JournalActa Mathematica Hungarica
Volume116
Issue number1-2
DOIs
Publication statusPublished - Jul 1 2007

Keywords

  • Biadditive function
  • Jensen-affine function
  • Linear functional equation
  • P-Wright affine function

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Daróczy, Z., Lajkó, K., Lovas, R. L., Maksa, G., & Páles, Z. (2007). Functional equations involving means. Acta Mathematica Hungarica, 116(1-2), 79-87. https://doi.org/10.1007/s10474-007-5296-2