Equality of two-variable functional means generated by different measures

László Losonczi, Zsolt Páles

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider two-variable functional means of the form where f, g are continuous functions on a real interval such that g is positive, f/g is strictly monotonic and μ is a measure over the Borel sets of [0,1]. The main results concern the functional equation Mf,g;μ = Mf,g;ν for the unknown functions f, g, where μ and ν are given measures. Depending on the symmetry properties of the measures, various necessary conditions and sufficient conditions are established.

Original languageEnglish
Pages (from-to)31-53
Number of pages23
JournalAequationes Mathematicae
Volume81
Issue number1
DOIs
Publication statusPublished - Feb 1 2011

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Keywords

  • Functional means
  • equality problem of means
  • functional equation
  • symmetric means

ASJC Scopus subject areas

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

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