Report of Meeting. The Twentieth Debrecen-Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), January 29-February 1, 2020
Abstract
Report of Meeting. The Twentieth Debrecen-Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), January 29-February 1, 2020.
Keywords
functional equations and inequalities; means; stability; Hermite-Hadamard type inequalities
References
1. T. Akhobadze, On the convergence of generalized Cesàro means of trigonometric Fourier series. I, Acta Math. Hungar. 115 (2007), 59–78.
2. M. Bajraktarević, Sur une équation fonctionnelle aux valeurs moyennes, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 13 (1958), 243–248.
3. K. Baron, On additive involutions and Hamel bases, Aequationes Math. 87 (2014), 159–163.
4. K. Baron and P. Volkmann, Dense sets of additive functions, Seminar LV, No. 16 (2003), 4 pp. http://www.math.us.edu.pl/smdk.
5. M. Bessenyei and Zs. Páles, Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl. 6 (2003), 379–392.
6. M. Bessenyei and Zs. Páles, Characterization of higher order monotonicity via integral inequalities, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 723–736.
7. Z. Boros and E. Garda-Mátyás, Conditional equations for quadratic functions, Acta Math. Hungar. 154 (2018), 389–401.
8. Z. Boros and E. Garda-Mátyás, Conditional equations for monomial functions, submitted.
9. Z. Boros and E. Gselmann, Hyers-Ulam stability of derivations and linear functions, Aequationes Math. 80 (2010), 13–25.
10. P. Carter and D. Lowry-Duda, On functions whose mean value abscissas are midpoints, with connections to harmonic functions, Amer. Math. Monthly 124 (2017), 535–542.
11. A. Dinghas, Zur Theorie der gewöhnlichen Differentialgleichungen, Ann. Acad. Sci. Fenn. Ser. A I No. 375 (1966), 19 pp.
12. M. Eshaghi Gordji and H. Khodaei, On the generalized Hyers-Ulam-Rassias stability of quadratic functional equations, Abstr. Appl. Anal. 2009, Art. ID 923476, 11 pp.
13. E. Garda-Mátyás, Quadratic functions fulfilling an additional condition along hyperbolas or the unit circle, Aequationes Math. 93 (2019), 451–465.
14. Gy. Gát and U. Goginava, Maximal operators of Cesàro means with varying parameters of Walsh-Fourier series, Acta Math. Hungar. 159 (2019), 653–668.
15. Gy. Gát and U. Goginava, Almost everywhere convergence and divergence of Cesàro means with varying parameters of Walsh-Fourier series, Mat. Sb. To appear.
16. R. Ger, Additivity and exponentiality are alien to each other, Aequationes Math. 80 (2010), 111–118.
17. G.H. Hardy and J.E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1934 (first edition), 1952 (second edition).
18. http://istcim.math.us.edu.pl/ISTCM_2019_problems.pdf, Katowice (2019).
19. W. Jabłoński, Additive involutions and Hamel bases, Aequationes Math. 89 (2015), 575–582.
20. W. Jabłoński, Additive iterative roots of identity and Hamel bases, Aequationes Math. 90 (2016), 133–145.
21. W. Jabłoński, A characterization of additive iterative roots of identity with respect to invariant subspaces, Aequationes Math. 93 (2019), 247–255.
22. M. Kałuszka and M. Krzeszowiec, Pricing insurance contracts under Cumulative Prospect Theory, Insurance Math. Econom. 50 (2012), 159–166.
23. C.I. Kim, G. Han and S.-A. Shim, Hyers-Ulam stability for a class of quadratic functional equations via a typical form, Abstr. Appl. Anal. 2013, Art. ID 283173, 8 pp.
24. E.B. Leach and M.C. Sholander, Multivariable extended mean values, J. Math. Anal. Appl. 104 (1984), 390–407.
25. R. Łukasik, A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), 961–965.
26. R. Łukasik, Some orthogonality equation with two functions, Miskolc Math. Notes 18 (2017), 953–960.
27. R. Łukasik and P. Wójcik, Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), 495–499.
28. R. Łukasik and P. Wójcik, A functional equation preserving the biadditivity, Results Math., accepted.
29. J. Matkowski, Integrable solutions of functional equations, Dissertationes Math. (Rozprawy Mat.) 127 (1975), 68 pp.
30. J. Morawiec and T. Zürcher, An application of functional equations for generating ε-invariant measures, J. Math. Anal. Appl. 476 (2019), 759–772.
31. J. Morawiec and T. Zürcher, Some classes of linear operators involved in functional equations, Ann. Funct. Anal. 10 (2019), 381–394.
32. S. Mortola and R. Peirone, The Sum of Periodic Functions, Topology Atlas Preprint #328.
33. C.T. Ng and W. Zhang, An algebraic equation for linear operators, Linear Algebra Appl. 412 (2006), 303–325.
34. K. Nikodem, On ϵ-invariant measures and a functional equation, Czechoslovak Math. J. 41(116) (1991), 565–569.
35. A. Nishiyama and S. Horinouchi, On a system of functional equations, Aequationes Math. 1 (1968), 1–5.
36. Zs. Páles and P. Pasteczka, Characterization of the Hardy property of means and the best Hardy constants, Math. Inequal. Appl. 19 (2016), 1141–1158.
37. Zs. Páles and P. Pasteczka, On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means, Math. Inequal. Appl. 21 (2018), 585–599.
38. Zs. Páles and P. Pasteczka, On Hardy-type inequalities for weighted means, Banach J. Math. Anal. 13 (2019), 217–233.
39. Zs. Páles and P. Pasteczka, On the homogenization of means, Acta Math. Hungar. 159 (2019), 537–562.
40. Zs. Páles and P. Pasteczka, On Hardy type inequalities for weighted quasideviation means, Math. Inequal. Appl. To appear.
41. T. Rajba, On a generalization of a theorem of Levin and Stečkin and inequalities of the Hermite-Hadamard type, Math. Inequal. Appl. 20 (2017), 363–375.
42. M. Sablik, An elementary method of solving functional equations, Ann. Univ. Sci. Budapest. Sect. Comput. 48 (2018), 181–188.
43. M.M. Sadr, Decomposition of functions between Banach spaces in the orthogonality equation, Aequationes Math. 91 (2017), 739–743.
44. M. Shaked and J.G. Shanthikumar, Stochastic Orders, Springer, New York, 2007.
45. P. Wójcik, On an orthogonality equation in normed spaces, Funct. Anal. Appl. 52 (2018), 224–227.
2. M. Bajraktarević, Sur une équation fonctionnelle aux valeurs moyennes, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 13 (1958), 243–248.
3. K. Baron, On additive involutions and Hamel bases, Aequationes Math. 87 (2014), 159–163.
4. K. Baron and P. Volkmann, Dense sets of additive functions, Seminar LV, No. 16 (2003), 4 pp. http://www.math.us.edu.pl/smdk.
5. M. Bessenyei and Zs. Páles, Hadamard-type inequalities for generalized convex functions, Math. Inequal. Appl. 6 (2003), 379–392.
6. M. Bessenyei and Zs. Páles, Characterization of higher order monotonicity via integral inequalities, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 723–736.
7. Z. Boros and E. Garda-Mátyás, Conditional equations for quadratic functions, Acta Math. Hungar. 154 (2018), 389–401.
8. Z. Boros and E. Garda-Mátyás, Conditional equations for monomial functions, submitted.
9. Z. Boros and E. Gselmann, Hyers-Ulam stability of derivations and linear functions, Aequationes Math. 80 (2010), 13–25.
10. P. Carter and D. Lowry-Duda, On functions whose mean value abscissas are midpoints, with connections to harmonic functions, Amer. Math. Monthly 124 (2017), 535–542.
11. A. Dinghas, Zur Theorie der gewöhnlichen Differentialgleichungen, Ann. Acad. Sci. Fenn. Ser. A I No. 375 (1966), 19 pp.
12. M. Eshaghi Gordji and H. Khodaei, On the generalized Hyers-Ulam-Rassias stability of quadratic functional equations, Abstr. Appl. Anal. 2009, Art. ID 923476, 11 pp.
13. E. Garda-Mátyás, Quadratic functions fulfilling an additional condition along hyperbolas or the unit circle, Aequationes Math. 93 (2019), 451–465.
14. Gy. Gát and U. Goginava, Maximal operators of Cesàro means with varying parameters of Walsh-Fourier series, Acta Math. Hungar. 159 (2019), 653–668.
15. Gy. Gát and U. Goginava, Almost everywhere convergence and divergence of Cesàro means with varying parameters of Walsh-Fourier series, Mat. Sb. To appear.
16. R. Ger, Additivity and exponentiality are alien to each other, Aequationes Math. 80 (2010), 111–118.
17. G.H. Hardy and J.E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1934 (first edition), 1952 (second edition).
18. http://istcim.math.us.edu.pl/ISTCM_2019_problems.pdf, Katowice (2019).
19. W. Jabłoński, Additive involutions and Hamel bases, Aequationes Math. 89 (2015), 575–582.
20. W. Jabłoński, Additive iterative roots of identity and Hamel bases, Aequationes Math. 90 (2016), 133–145.
21. W. Jabłoński, A characterization of additive iterative roots of identity with respect to invariant subspaces, Aequationes Math. 93 (2019), 247–255.
22. M. Kałuszka and M. Krzeszowiec, Pricing insurance contracts under Cumulative Prospect Theory, Insurance Math. Econom. 50 (2012), 159–166.
23. C.I. Kim, G. Han and S.-A. Shim, Hyers-Ulam stability for a class of quadratic functional equations via a typical form, Abstr. Appl. Anal. 2013, Art. ID 283173, 8 pp.
24. E.B. Leach and M.C. Sholander, Multivariable extended mean values, J. Math. Anal. Appl. 104 (1984), 390–407.
25. R. Łukasik, A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), 961–965.
26. R. Łukasik, Some orthogonality equation with two functions, Miskolc Math. Notes 18 (2017), 953–960.
27. R. Łukasik and P. Wójcik, Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), 495–499.
28. R. Łukasik and P. Wójcik, A functional equation preserving the biadditivity, Results Math., accepted.
29. J. Matkowski, Integrable solutions of functional equations, Dissertationes Math. (Rozprawy Mat.) 127 (1975), 68 pp.
30. J. Morawiec and T. Zürcher, An application of functional equations for generating ε-invariant measures, J. Math. Anal. Appl. 476 (2019), 759–772.
31. J. Morawiec and T. Zürcher, Some classes of linear operators involved in functional equations, Ann. Funct. Anal. 10 (2019), 381–394.
32. S. Mortola and R. Peirone, The Sum of Periodic Functions, Topology Atlas Preprint #328.
33. C.T. Ng and W. Zhang, An algebraic equation for linear operators, Linear Algebra Appl. 412 (2006), 303–325.
34. K. Nikodem, On ϵ-invariant measures and a functional equation, Czechoslovak Math. J. 41(116) (1991), 565–569.
35. A. Nishiyama and S. Horinouchi, On a system of functional equations, Aequationes Math. 1 (1968), 1–5.
36. Zs. Páles and P. Pasteczka, Characterization of the Hardy property of means and the best Hardy constants, Math. Inequal. Appl. 19 (2016), 1141–1158.
37. Zs. Páles and P. Pasteczka, On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means, Math. Inequal. Appl. 21 (2018), 585–599.
38. Zs. Páles and P. Pasteczka, On Hardy-type inequalities for weighted means, Banach J. Math. Anal. 13 (2019), 217–233.
39. Zs. Páles and P. Pasteczka, On the homogenization of means, Acta Math. Hungar. 159 (2019), 537–562.
40. Zs. Páles and P. Pasteczka, On Hardy type inequalities for weighted quasideviation means, Math. Inequal. Appl. To appear.
41. T. Rajba, On a generalization of a theorem of Levin and Stečkin and inequalities of the Hermite-Hadamard type, Math. Inequal. Appl. 20 (2017), 363–375.
42. M. Sablik, An elementary method of solving functional equations, Ann. Univ. Sci. Budapest. Sect. Comput. 48 (2018), 181–188.
43. M.M. Sadr, Decomposition of functions between Banach spaces in the orthogonality equation, Aequationes Math. 91 (2017), 739–743.
44. M. Shaked and J.G. Shanthikumar, Stochastic Orders, Springer, New York, 2007.
45. P. Wójcik, On an orthogonality equation in normed spaces, Funct. Anal. Appl. 52 (2018), 224–227.
AMSilR. (2020). Report of Meeting. The Twentieth Debrecen-Katowice Winter Seminar on Functional Equations and Inequalities Hajdúszoboszló (Hungary), January 29-February 1, 2020. Annales Mathematicae Silesianae, 34(2), 286-304. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13625
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