November 6 (10:00-11:00) room C.510 (new building, 5th floor)
Gergely Kiss (Corvinus University)
Quasi-arithmetic means, quasi-sums, and bisymmetry with and without regularity assumption
Bisymmetry equation first appears in works of János Aczél, where it gains importance in the characterization of quasi-arithmetic means. The original proof of Aczél is based on the assumption of continuity. We proved that the continuity assumption can be eliminated from the above-mentioned characterization. As a consequence of our results, we found a dichotomy theorem for the symmetric assumption of bisymmetric, strictly monotonic, and reflexive functions. I will also present a construction that, among other significant consequences, demonstrates that continuity in Aczél’s theorem on quasi-sums might not be eliminated. Finally, I will outline some open directions of research.
The talk is partially based on joint works with Pál Burai and Patricia Szokol.