Leírás
The next analysis seminar will be on Thursday, 3 October at usual time 12:15 and place Tondos Lecture Room.
The talk will be given by Patrícia Szokol (Debrecen) with title and abstract
Characterization of quasi-arithmetic means without regularity condition
We focus on the characterization theorem of János Aczél (1948) on quasi-arithmetic means. He proved that every continuous, bisymmetric, symmetric, reflexive, strictly monotonic binary map on a proper interval is a quasi-arithmetic mean.
Our first goal is to show a somewhat surprising result, namely, the purely algebraic bisymmetry property has a regularity improving feature. More precisely, our first theorem shows that the continuity property in the original theorem is redundant.
As a continuation of this result, we demonstrate that it can be refined in the way that the symmetry condition can be weakened by assuming symmetry only for a pair of distinct points of an interval.
The presentation is based on joint papers with Pál Burai and Gergely Kiss.