aequationes mathematicae

, Volume 32, Issue 1, pp 171–194 | Cite as

On the characterization of quasiarithmetic means with weight function

  • Zsolt Páles
Research Papers


In the present note we completely solve the characterization problem of quasiarithmetic means with weight function, that is, functions of the form
$$M(x_1 ,...,x_n ) = f^{ - 1} \left( {\sum\limits_{i = 1}^n {p(x_i )} f(x_i )/\sum\limits_{i = 1}^n {p(x_i )} } \right)$$
(f is a strictly monotonic continuous real function andp 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].

AMS (1980) subject classification

Primary 39C05 Secondary 26B99 26D99 


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Copyright information

© Birkhäuser Verlag 1987

Authors and Affiliations

  • Zsolt Páles
    • 1
  1. 1.Department of MathematicsKossuth Lajos University, Pf. 12DebrecenHungary

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