(Budapest Corvinus University oraz R\u00e9nyi Alfr\u00e9d Institute of Mathematics). Doktor Kiss wyg\u0142osi w tych dniach dwa odczyty w ramach regularnie organizowanych w naszym Instytucie seminari\u00f3w z zakresu r\u00f3wna\u0144 i nier\u00f3wno\u015bci funkcyjnych.<\/span><\/span><\/p>\nNa wyk\u0142ady serdecznie zapraszamy wszystkich zainteresowanych. Poni\u017cej zamieszczamy szczeg\u00f3\u0142y organizacyjne oraz streszczenia obydwu odczyt\u00f3w.<\/span><\/p>\n
\nSeminarium z r\u00f3wna\u0144 i nier\u00f3wno\u015bci funkcyjnych o wielu zmiennych<\/span><\/strong><\/p>\n15 grudnia 2025 r. (poniedzia\u0142ek), godz. 16:15, sala 553<\/strong><\/span> <\/span><\/span><\/p>\nTytu\u0142 odczytu: <\/span><\/span><\/strong>Quasi-arithmetic means and quasi-sums vs. bisymmetry and associativity with and without regularity assumption<\/em><\/span><\/span><\/p>\nStreszczenie:<\/span><\/strong> Bisymmetry equation first appears in works of J\u00e1nos Acz\u00e9l, where it gains importance in the characterization of quasi-arithmetic means. The original proof of Acz\u00e9l 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 Acz\u00e9l’s theorem on quasi-sums can not be eliminated. Finally, I will outline some open directions of research.<\/span><\/span><\/p>\n
\nSeminarium z r\u00f3wna\u0144 funkcyjnych<\/span><\/strong><\/p>\n16 grudnia 2025 r. (wtorek), godz. 16:15, sala 553<\/strong><\/span> <\/span><\/p>\nTytu\u0142 odczytu: <\/span><\/span><\/strong>Polynomial equations of additive functions<\/em><\/span><\/span><\/p>\nStreszczenie:<\/span><\/strong> By a polynomial equation of additive functions we mean <\/span><\/span>![](\"https:\/\/latex.codecogs.com\/gif.latex?P(f_1^{r_1}(x^{s_1}),)
, <\/span>where ![](\"https:\/\/latex.codecogs.com\/gif.latex?)
is a polynomial in n variables, r\u1d62 and s\u1d62 are positive integers, and the f\u1d62 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. <\/span>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 r\u1d62 and s\u1d62, lead to explicit descriptions of all solutions. <\/span>However, no general technique is currently known to resolve the problem in full generality. <\/span><\/span>Finally, we pose several questions concerning the degree of the solutions in a special class of polynomial equations recently studied jointly with E. Gselmann.<\/span><\/span><\/p>\n[\/vc_column_text][\/vc_column][vc_column width=”1\/3″][vc_single_image image=”7798″ img_size=”318×429″ add_caption=”yes” alignment=”center” onclick=”link_image”][\/vc_column][\/vc_row]<\/p>","protected":false},"excerpt":{"rendered":"
[vc_row][vc_column width=”2\/3″][vc_column_text] Z przyjemno\u015bci\u0105 informujemy, \u017ce w dniach 15 i 16 grudnia 2025 r. w Instytucie Matematyki go\u015bci\u0142 b\u0119dzie Dr. Gergely Kiss (Budapest Corvinus University oraz R\u00e9nyi Alfr\u00e9d Institute of Mathematics). Doktor Kiss wyg\u0142osi w tych dniach dwa odczyty w ramach regularnie organizowanych w naszym Instytucie seminari\u00f3w z zakresu r\u00f3wna\u0144 i nier\u00f3wno\u015bci funkcyjnych. Na wyk\u0142ady […]<\/p>\n
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