Online premeans and their computation complexity

Abstract

We extend some approach to a family of symmetric means (i.e. symmetric functions M : ∞ n=1 I n → I with min ≤ M ≤ max; I is an interval). Namely, it is known that every symmetric mean can be written in a formand continuous functions f and F we obtain two series of families (depending on k). It can be treated as a measure of complexity in a family of means (this idea is inspired by theory of regular languages and algorithmics).As a result we characterize celebrated families of quasi-arithmetic means (G = R × Z) and Bajraktarević means (G = R 2 under some additional assumptions). Moreover, we establish certain estimations of complexity for several other classical families.