Report of Meeting. The Twenty-second Debrecen–Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), February 1–4, 2023

A.H. Ali and Zs. Páles, Taylor-type expansions in terms of exponential polynomials, Math. Inequal. Appl. 25 (2022), no. 4, 1123–1141.

M. Baczyński, W. Fechner, and S. Massanet, A functional equation stemming from a characterization of power-based implications, in: 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), IEEE, 2019, pp. 1–6.

M. Baczyński, W. Fechner, and S. Massanet, On a generalization of multiplicative Sincov’s equation for fuzzy implication functions, Fuzzy Sets and Systems 451 (2022), 196–205.

M. Bajraktarević, Sur une équation fonctionnelle aux valeurs moyennes, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 13 (1958), 243–248.

M. Bajraktarević, Sur une généralisation des moyennes quasilinéaires, Publ. Inst. Math. (Beograd) (N.S.) 3(17) (1963), 69–76.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.

K. Baron, J. Matkowski, and K. Nikodem, A sandwich with convexity, Math. Pannon. 5 (1994), no. 1, 139–144.

K. Baron and J. Wesołowski, From invariance under binomial thinning to unification of the Cauchy and the Gołąb–Schinzel-type equations, Results Math. 76 (2021), Paper No. 168, 14 pp.

A. Barvinok, A Course in Convexity, Graduate Studies in Mathematics, 54, American Mathematical Society, Providence, RI, 2002.

C. Bennett and R. Sharpley, Interpolation of Operators, Pure and Applied Mathematics, 129, Academic Press, Inc., Boston, MA, 1988.

M. Bessenyei, G. Horváth, and Cs.G. Kézi, Functional equations on finite groups of substitutions, Expo. Math. 30 (2012), no. 3, 283–294.

M. Bessenyei, Á. Konkoly, and G. Szabó, Linear functional equations involving finite substitutions, Acta Sci. Math. (Szeged) 83 (2017), no. 1–2, 71–81.

M. Bessenyei and Zs. Páles, Applications of the Bielecki renorming technique, J. Fixed Point Theory Appl. 23 (2021), no. 2, Paper No. 15, 23 pp.

M. Bessenyei and E. Pénzes, Generalized fractals in semimetric spaces, Nonlinear Anal. 220 (2022), Paper No. 112853, 15 pp.

A. Bielecki, Une remarque sur la méthode de Banach–Cacciopoli–Tikhonov dans la théorie des équations différentielles ordinaires, Bull. Acad. Polon. Sci. Cl. III. 4 (1956), 261–264.

Z. Boros, Strongly ℚ-differentiable functions, Real Anal. Exchange 27 (2001/02), no. 1, 17–25.

Z. Boros and P. Tóth, Strong geometric derivatives, Abstract of presentation by P. Tóth during the 22nd DKWS (the 22nd Debrecen–Katowice Winter Seminar, Hajdúszoboszló, Hungary, February 1–4, 2023).

G.Gy. Borus and A. Gilányi, Solving systems of linear functional equations with computer, 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), IEEE, 2013, 559–562.

G.Gy. Borus and A. Gilányi, Computer assisted solution of systems of two variable linear functional equations, Aequationes Math. 94 (2020), no. 4, 723–736.

J.M. Borwein and A.S. Lewis, Convex Analysis and Nonlinear Optimization. Theory and Examples, 2nd ed., CMS Books in Mathematics, 3, Springer, New York, 2006.

D. Broszka and Z. Grande, On I-differentiation, Tatra Mt. Math. Publ. 35 (2007), 25–40.

H. Bühlmann, Mathematical Models in Risk Theory, Springer-Verlag, Berlin, 1970.

L. Carleson, Appendix to the paper by J.-P. Kahane and Y. Katznelson, in: P. Erdős et al. (eds.), Studies in Pure Mathematics, Birkhäuser, Basel-Boston, 1983, pp. 411–413.

Z. Daróczy and M. Laczkovich, On functions taking the same value on many pairs of points, Real Anal. Exchange 33 (2007/2008), no. 2, 385–394.

Z. Daróczy and Gy. Maksa, Functional equations on convex sets, Acta Math. Hungar. 68 (1995), no. 3, 187–195.

Z. Daróczy and Zs. Páles, Gauss-composition of means and the solution of the Matkowski–Sutô problem, Publ. Math. Debrecen 61 (2002), no. 1–2, 157–218.

Z. Daróczy and V. Totik, Remarks on a functional equation, Acta Sci. Math. (Szeged) 81 (2015), no. 3–4, 527–534.

J. Dhombres, Relations de dépendance entre les équations fonctionnelles de Cauchy, Aequationes Math. 35 (1988), no. 2-3, 186–212.

D.E. Edmunds and W.D. Evans, Hardy Operators, Function Spaces and Embeddings, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2004.

J. Farkas, Theorie der einfachen Ungleichungen, J. Reine Angew. Math. 124 (1902), 1–27.

G. Fechner, Elements of Psychophysics, Holt, Rinehart & Winston, New York, 1966. (Original work published 1860.)

W. Förg-Rob, K. Nikodem, and Zs. Páles, Separation by monotonic functions, Math. Pannon. 7 (1996), no. 2, 191–196.

G. Gát, Cesàro means of subsequences of partial sums of trigonometric Fourier series, Constr. Approx. 49 (2019), no. 1, 59–101.

G. Gát, Almost everywhere divergence of Cesàro means of subsequences of partial sums of trigonometric Fourier series, submitted.

J. Ger, On Sahoo-Riedel equations on a real interval, Aequationes Math. 63 (2002), no. 1–2, 168–179.

R. Ger and M. Sablik, Alien functional equations: a selective survey of results, in: J. Brzdęk et al. (eds.), Developments in Functional Equations and Related Topics, Springer Optim. Appl. 124, Springer, Cham, 2017, pp. 107–147.

A. Gilányi, Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Diss., Universität Karlsruhe, Karlsruhe, Germany, 1995.

A. Gilányi, Alienness of linear functional equations, The Nineteenth Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities, Zakopane (Poland), January 30 – February 2, 2019, Ann. Math. Sil. 33 (2019), p. 311.

D. Gronau, A remark on Sincov’s functional equation, Notices of the South African Mathematical Society 31 (2000), no.1, 1–8.

R. Grünwald and Zs. Páles, On the equality problem of generalized Bajraktarević means, Aequationes Math. 94 (2020), no. 4, 651–677.

R. Grünwald and Zs. Páles, Local and global inequalities for nonsymmetric generalized Bajraktarević means, manuscript.

G.J. Iverson, Analytical methods in the theory of psychophysical discrimination. II: the near-miss to Weber’s law, Falmagne’s law, the psychophysical power law and the law of similarity, J. Math. Psych. 50 (2006), no. 3, 283–289.

J.-P. Kahane and Y. Katznelson, Séries de Fourier des fonctions bornées, in: P. Erdős et al. (eds.), Studies in Pure Mathematics, Birkhäuser, Basel-Boston, 1983, pp. 395–410.

T. Kiss and Zs. Páles, On a functional equation related to two-variable Cauchy means, Math. Inequal. Appl. 22 (2019), no. 4, 1099–1122.

B. Koclęga-Kulpa and T. Szostok, On some functional equations connected to Hadamard inequalities, Aequationes Math. 75 (2008), 119–129.

Z. Kominek, L. Reich, and J. Schwaiger, On additive functions fulfilling some additional condition, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 35–42 (1999).

S. Massanet, J. Recasens, and J. Torrens, Some characterizations of T-power based implications, Fuzzy Sets and Systems 359 (2019), 42–62.

G.M. Molnár and Zs. Páles, On convex and concave sequences and their applications, Math. Inequal. Appl. 25 (2022), no. 3, 727–750.

C.T. Ng, Functions generating Schur-convex sums, in: W.Walter (ed.), General Inequalities 5: 5th International Conference on General Inequalities, Oberwolfach, May 4–10, 1986, Internat. Schriftenreihe Numer. Math. 80, Birkhäuser, Basel, 1987, pp. 433–438.

K. Nikodem, Approximately quasiconvex functions, C. R. Math. Rep. Acad. Sci. Canada 10 (1988), no. 6, 291–294.

Zs. Páles and P. Pasteczka, On the Jensen convex and Jensen concave envelopes of means, Arch. Math. (Basel) 116 (2021), no. 4, 423–432.

Zs. Páles and A. Zakaria, On the local and global comparison of generalized Bajraktarević means, J. Math. Anal. Appl. 455 (2017), no. 1, 792–815.

I. Pawlikowska, A method of solving functional equations on convex subsets of linear spaces, Aequationes Math. 75 (2008), no. 1–2, 1–28.

C.E.M. Pearce and A.M. Rubinov, P-functions, quasi-convex functions, and Hadamardtype inequalities, J. Math. Anal. Appl. 240 (1999), no. 1, 92–104.

S.B. Prešić, Méthode de résolution d’une classe d’équations fonctionnelles linéaires, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Math. Fiz. No. 119 (1963), 21–28.

S.B. Prešić, Sur l’équation fonctionnelle f(x) = H(x, f(x), f(θ_2x),..., f(θ_nx)), Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Math. Fiz. No. 118 (1963), 17–20.

Problem 12347, Amer. Math. Monthly 129 (2022), no. 8, p. 786.

R.T. Rockafellar, Convex Analysis, Princeton Mathematical Series, 28, Princeton University Press, Princeton, N.J., 1970.

S. Rolewicz, On γ-paraconvex multifunctions, Math. Japon. 24 (1979), 293–300.

P.K. Sahoo and T. Riedel, Mean Value Theorems and Functional Equations, World Scientific, Singapore–New Jersey–London–Hong Kong, 1998.

L. Székelyhidi, On a class of linear functional equations, Publ. Math. Debrecen 29 (1982), no. 1-2, 19–28.

L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific Publishing Co., Inc., Teaneck, NJ, 1991.

D.M. Sincov, Bemerkungen über Funktionalrechnung, (Russian), Bull. Soc. Phys.-Math. Kazan (2) 13 (1903), 48–72.

T. Szostok, Alienation of two general linear functional equations, Aequationes Math. 94 (2020), no. 2, 287–301.

A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285–309.

A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, J. Risk Uncertain. 5 (1992), no. 4, 297–323.

R.J. Vanderbei, Linear Programming. Foundations and Extensions, 4th ed., International Series in Operations Research & Management Science, 196, Springer, New York, 2014.

H.A. Voloshyn and V.K. Maslyuchenko, The topologization of the space of separately continuous functions, Carpathian Math. Publ. 5 (2013), no. 2, 199–207.

H.A. Voloshyn, V.K. Maslyuchenko, and O.V. Maslyuchenko, Embedding of the space of separately continuous functions into the product of Banach spaces and its barrelledness, Mathematical Bulletin of Shevchenko Scientific Society 11 (2014), 36–50.

H.A. Voloshyn, V.K. Maslyuchenko, and O.V. Maslyuchenko, The bornologicity of the space of separately continuous functions, Mathematical Bulletin of Taras Shevchenko Scientific Society 12 (2015), 61–67.

H.A. Voloshyn, V.K. Maslyuchenko, and O.V. Maslyuchenko, On Baireness of the space of separately continuous function, Transactions of Institute of Mathematics, the NAS of Ukraine 12 (2015), no. 3, 78–96.

E.M. Wright, An inequality for convex functions, Amer. Math. Monthly 61 (1954), 620–622.