In this paper we characterize generalized quasi-arithmetic means, that is means of the form M(x1,.., xn):= (f1 + • • • + fn)-1(f1(x1) + • • • + fn(xn)), where f1,.., fn: I → R are strictly increasing and continuous functions. Our characterization involves the Gauss composition of the cyclic meantype mapping induced by M and a generalized bisymmetry equation.
- Generalized quasi-arithmetic mean
ASJC Scopus subject areas
- Applied Mathematics