Z przyjemnością informujemy, że w dniach 15 i 16 grudnia 2025 r. w Instytucie Matematyki gościł będzie Dr. Gergely Kiss (Budapest Corvinus University oraz Rényi Alfréd Institute of Mathematics). Doktor Kiss wygłosi w tych dniach dwa odczyty w ramach regularnie organizowanych w naszym Instytucie seminariów z zakresu równań i nierówności funkcyjnych.
Na wykłady serdecznie zapraszamy wszystkich zainteresowanych. Poniżej zamieszczamy szczegóły organizacyjne oraz streszczenia obydwu odczytów.
Seminarium z równań i nierówności funkcyjnych o wielu zmiennych
15 grudnia 2025 r. (poniedziałek), godz. 16:15, sala 553
Tytuł odczytu: Quasi-arithmetic means and quasi-sums vs. bisymmetry and associativity with and without regularity assumption
Streszczenie: 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, reflexive functions. I will also present a construction that, among other significant consequences, demonstrates that continuity in Aczél’s theorem on quasi-sums can not be eliminated. Finally, I will outline some open directions of research.
Seminarium z równań funkcyjnych
16 grudnia 2025 r. (wtorek), godz. 16:15, sala 553
Tytuł odczytu: Polynomial equations of additive functions
Streszczenie: By a polynomial equation of additive functions we mean , where
is a polynomial in n variables, rᵢ and sᵢ are positive integers, and the fᵢ are unknown additive functions. We present characterizations of the solutions for several notable special cases, including the Ebanks-type equations and their multiplicative analogues. Furthermore, we discuss two key structural principles of our method that can be applied to more general polynomial equations under reasonable restrictions. One of them is the symmetrization method, based on the polarization formula, and the other relies on the theory of decomposable functions, originating from the work of E. Shulman and M. Laczkovich. These principles ensure that the solutions can be sought among polynomial-exponential functions defined on suitable subfields of C, which, for certain choices of the parameters rᵢ and sᵢ, lead to explicit descriptions of all solutions. However, no general technique is currently known to resolve the problem in full generality. Finally, we pose several questions concerning the degree of the solutions in a special class of polynomial equations recently studied jointly with E. Gselmann.
