ACTA issues

Characterization of generalized quasi-arithmetic means

Janusz Matkowski, Zsolt Páles

Acta Sci. Math. (Szeged) 81:3-4(2015), 447-456

Abstract. In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,\dots,x_n):=(f_1+\cdots +f_n)^{-1}(f_1(x_1)+\cdots +f_n(x_n))$, where $f_1,\dots,f_n\colon I\to{\msbm R} $ are strictly increasing and continuous functions. Our characterization involves the Gauss composition of the cyclic mean-type mapping induced by $M$ and a generalized bisymmetry equation.

DOI: 10.14232/actasm-015-028-7

AMS Subject Classification (1991): 39B40

Keyword(s): generalized quasi-arithmetic mean, bisymmetry, characterization

Received April 9, 2015, and in revised form June 2, 2015. (Registered under 28/2015.)