On the characterization of quasiarithmetic means with weight function

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Abstract

In the present note we completely solve the characterization problem of quasiarithmetic means with weight function, that is, functions of the form {Mathematical expression} (f is a strictly monotonic continuous real function and p is a positive valued real function.) The result obtained gives a partial answer to a 22-year-old problem of Aczél [1] and generalizes the characterization theorem of quasiarithmetic means which is due to Kolmogorov [8], Nagumo [9] and de Finetti [7].

Original languageEnglish
Pages (from-to)171-194
Number of pages24
JournalAequationes Mathematicae
Volume32
Issue number1
DOIs
Publication statusPublished - Dec 1987

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Quasi-arithmetic Mean
Weight Function
Characterization Theorem
Monotonic
Strictly
Partial
Generalise

Keywords

  • AMS (1980) subject classification: Primary 39C05, Secondary 26B99, 26D99

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the characterization of quasiarithmetic means with weight function. / Páles, Z.

In: Aequationes Mathematicae, Vol. 32, No. 1, 12.1987, p. 171-194.

Research output: Contribution to journalArticle

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