On axiomizing and extending the quasi-arithmetic mean

Abstract

Quasi-arithmetic means contain many other mean value concepts such as the arithmetic, the geometric or the harmonic mean as special cases. Treating quasi-arithmetic means as sequences of mappings from I^n into I (for some real interval I) this paper shows that under mild additional conditions this mapping is uniquely determined by its values on I^2. This extends a well-known result by Huntington [4] where this claim is proven only for special cases.