Report of Meeting. The Nineteenth Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Zakopane (Poland), January 30–February 2, 2019
Abstract
Report of Meeting. The Nineteenth Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Zakopane (Poland), January 30–February 2, 2019.
Keywords
functional equations and inequalities; convex functions; means
References
1. J. Aczél, A mean value property of the derivative of quadratic polynomials – without mean values and derivatives, Math. Mag. 58 (1985), no. 1, 42–45.
2. T. Akhobadze, On the convergence of generalized Cesàro means of trigonometric Fourier series. I, Acta Math. Hungar. 115 (2007), no. 1–2, 59–78.
3. H. Alzer and St. Ruscheweyh, On the intersection of two-parameter mean value families, Proc. Amer. Math. Soc. 129 (2001), no. 9, 2655–2662.
4. M. Amou, Multiadditive functions satisfying certain functional equations, Aequationes Math. 93 (2019), 345–350.
5. M. Bajraktarević, Sur une équation fonctionnelle aux valeurs moyennes, Glasnik Mat.-Fiz. Astronom. Dru²tvo Mat. Fiz. Hrvatske. Ser. II 13 (1958), 243–248.
6. M. Bajraktarević, Über die Vergleichbarkeit der mit Gewichtsfunktionen gebildeten Mittelwerte, Studia Sci. Math. Hungar. 4 (1969), 3–8.
7. Z.M. Balogh, O.O. Ibrogimov and B.S. Mityagin, Functional equations and the Cauchy mean value theorem, Aequationes Math. 90 (2016), no. 4, 683–697.
8. K. Baron, On the convergence in law of iterates of random-valued functions, Aust. J. Math. Anal. Appl. 6 (2009), no. 1, Art. 3, 9 pp.
9. K. Baron and J. Morawiec, Lipschitzian solutions to linear iterative equations revisited, Aequationes Math. 91 (2017), 161–167.
10. 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.
11. P. Carter and D. Lowry-Duda, On functions whose mean value abscissas are midpoints, with connections to harmonic functions, Amer. Math. Monthly 124 (2017), no. 6, 535–542.
12. J. Dhombres, Relations de dépendance entre les équations fonctionnelles de Cauchy, Aequationes Math. 35 (1988), 186–212.
13. 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.
14. A. Gilányi, Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Diss., Universität Karlsruhe, Karlsruhe, Germany, 1995.
15. A. Gilányi, Solving linear functional equations with computer, Math. Pannon. 9 (1998), 57–70.
16. Sh. Haruki, A property of quadratic polynomials, Amer. Math. Monthly 86 (1979), no. 7, 577–579.
17. R. Kapica, The geometric rate of convergence of random iteration in the Hutchinson distance, Aequationes Math. 93 (2019), 149–160.
18. T. Kiss and Zs. Páles, On a functional equation related to two-variable weighted quasiarithmetic means, J. Difference Equ. Appl. 24 (2018), no. 1, 107–126.
19. T. Kiss and Zs. Páles, On a functional equation related to two-variable Cauchy means, Math. Inequal. Appl. 22 (2019).
20. M. Kuczma, B. Choczewski and R. Ger, Iterative functional equations, Encyclopedia of Mathematics and its Applications 32, Cambridge University Press, Cambridge, 1990.
21. E.B. Leach and M.C. Sholander, Multivariable extended mean values, J. Math. Anal. Appl. 104 (1984), no. 2, 390–407.
22. R. Łukasik, A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), no. 5, 961–965.
23. R. Łukasik, A note on functional equations connected with the Cauchy mean value theorem, Aequationes Math. 92 (2018), no. 5, 935–947.
24. R. Łukasik and P. Wójcik, Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), no. 3, 495–499.
25. A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Second edition, Springer Series in Statistics, New York–Dordrecht–Heidelberg–London, 2011.
26. K. Nikodem, On ϵ-invariant measures and a functional equation, Czechoslovak Math. J. 41 (1991), no. 4, 565–569.
27. A. Nishiyama and S. Horinouchi, On a system of functional equations, Aequationes Math. 1 (1968), 1–5.
28. A. Olbryś and T. Szostok, On T-Schur convex maps. Submitted.
29. Zs. Páles, On approximately convex functions, Proc. Amer. Math. Soc. 131 (2003), no. 1, 243–252.
30. M. Sablik, An elementary method of solving functional equations, Ann. Univ. Sci. Budapest. Sect. Comput. 48 (2018), 181–188.
31. P.K. Sahoo and T. Riedel, Mean Value Theorems and Functional Equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1998.
32. E. Shulman, Subadditive set-functions on semigroups, applications to group representations and functional equations, J. Funct. Anal. 263 (2012), no. 5, 1468–1484.
33. L. Székelyhidi, On a class of linear functional equations, Publ. Math. Debrecen 29 (1982), no. 1–2, 19–28.
34. L. Székelyhidi, On a linear functional equation, Aequationes Math. 38 (1989), no. 2–3, 113–122.
35. L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific Publishing Co., Teaneck, NJ, 1991.
36. L. Székelyhidi, On the extension of exponential polynomials, Math. Bohem. 125 (2000), no. 3, 365–370.
37. T. Szostok, Inequalities for convex functions via Stieltjes integral, Lith. Math. J. 58 (2018), no. 1, 95–103.
2. T. Akhobadze, On the convergence of generalized Cesàro means of trigonometric Fourier series. I, Acta Math. Hungar. 115 (2007), no. 1–2, 59–78.
3. H. Alzer and St. Ruscheweyh, On the intersection of two-parameter mean value families, Proc. Amer. Math. Soc. 129 (2001), no. 9, 2655–2662.
4. M. Amou, Multiadditive functions satisfying certain functional equations, Aequationes Math. 93 (2019), 345–350.
5. M. Bajraktarević, Sur une équation fonctionnelle aux valeurs moyennes, Glasnik Mat.-Fiz. Astronom. Dru²tvo Mat. Fiz. Hrvatske. Ser. II 13 (1958), 243–248.
6. M. Bajraktarević, Über die Vergleichbarkeit der mit Gewichtsfunktionen gebildeten Mittelwerte, Studia Sci. Math. Hungar. 4 (1969), 3–8.
7. Z.M. Balogh, O.O. Ibrogimov and B.S. Mityagin, Functional equations and the Cauchy mean value theorem, Aequationes Math. 90 (2016), no. 4, 683–697.
8. K. Baron, On the convergence in law of iterates of random-valued functions, Aust. J. Math. Anal. Appl. 6 (2009), no. 1, Art. 3, 9 pp.
9. K. Baron and J. Morawiec, Lipschitzian solutions to linear iterative equations revisited, Aequationes Math. 91 (2017), 161–167.
10. 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.
11. P. Carter and D. Lowry-Duda, On functions whose mean value abscissas are midpoints, with connections to harmonic functions, Amer. Math. Monthly 124 (2017), no. 6, 535–542.
12. J. Dhombres, Relations de dépendance entre les équations fonctionnelles de Cauchy, Aequationes Math. 35 (1988), 186–212.
13. 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.
14. A. Gilányi, Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Diss., Universität Karlsruhe, Karlsruhe, Germany, 1995.
15. A. Gilányi, Solving linear functional equations with computer, Math. Pannon. 9 (1998), 57–70.
16. Sh. Haruki, A property of quadratic polynomials, Amer. Math. Monthly 86 (1979), no. 7, 577–579.
17. R. Kapica, The geometric rate of convergence of random iteration in the Hutchinson distance, Aequationes Math. 93 (2019), 149–160.
18. T. Kiss and Zs. Páles, On a functional equation related to two-variable weighted quasiarithmetic means, J. Difference Equ. Appl. 24 (2018), no. 1, 107–126.
19. T. Kiss and Zs. Páles, On a functional equation related to two-variable Cauchy means, Math. Inequal. Appl. 22 (2019).
20. M. Kuczma, B. Choczewski and R. Ger, Iterative functional equations, Encyclopedia of Mathematics and its Applications 32, Cambridge University Press, Cambridge, 1990.
21. E.B. Leach and M.C. Sholander, Multivariable extended mean values, J. Math. Anal. Appl. 104 (1984), no. 2, 390–407.
22. R. Łukasik, A note on the orthogonality equation with two functions, Aequationes Math. 90 (2016), no. 5, 961–965.
23. R. Łukasik, A note on functional equations connected with the Cauchy mean value theorem, Aequationes Math. 92 (2018), no. 5, 935–947.
24. R. Łukasik and P. Wójcik, Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), no. 3, 495–499.
25. A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Second edition, Springer Series in Statistics, New York–Dordrecht–Heidelberg–London, 2011.
26. K. Nikodem, On ϵ-invariant measures and a functional equation, Czechoslovak Math. J. 41 (1991), no. 4, 565–569.
27. A. Nishiyama and S. Horinouchi, On a system of functional equations, Aequationes Math. 1 (1968), 1–5.
28. A. Olbryś and T. Szostok, On T-Schur convex maps. Submitted.
29. Zs. Páles, On approximately convex functions, Proc. Amer. Math. Soc. 131 (2003), no. 1, 243–252.
30. M. Sablik, An elementary method of solving functional equations, Ann. Univ. Sci. Budapest. Sect. Comput. 48 (2018), 181–188.
31. P.K. Sahoo and T. Riedel, Mean Value Theorems and Functional Equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1998.
32. E. Shulman, Subadditive set-functions on semigroups, applications to group representations and functional equations, J. Funct. Anal. 263 (2012), no. 5, 1468–1484.
33. L. Székelyhidi, On a class of linear functional equations, Publ. Math. Debrecen 29 (1982), no. 1–2, 19–28.
34. L. Székelyhidi, On a linear functional equation, Aequationes Math. 38 (1989), no. 2–3, 113–122.
35. L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific Publishing Co., Teaneck, NJ, 1991.
36. L. Székelyhidi, On the extension of exponential polynomials, Math. Bohem. 125 (2000), no. 3, 365–370.
37. T. Szostok, Inequalities for convex functions via Stieltjes integral, Lith. Math. J. 58 (2018), no. 1, 95–103.
AMSilR. (2019). Report of Meeting. The Nineteenth Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities Zakopane (Poland), January 30–February 2, 2019. Annales Mathematicae Silesianae, 33, 306-325. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13675
Redakcja AMSil
annales.math@us.edu.pl
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
