dr Zbigniew Leśniak

orcid.org/0000-0002-6717-6903

profesor UKEN (pracownik badawczo-dydaktyczny)

Katedra Analizy Matematycznej i Zastosowań

pokój:     110

telefon:     12 662-62-89

e-mail:     zbigniew.lesniak@uken.krakow.pl

prywatna strona www:     https://orcid.org/0000-0002-6717-6903

Harmonogram zajęć:

Harmonogram konsultacji:

Curriculum Vitae

Wykształcenie

1983-1988 Uniwersytet Jagielloński w Krakowie, Wydział Matematyki i Fizyki; studia na kierunku matematyka

Dyplomy

• 1988 magister matematyki (UJ). Tytuł pracy magisterskiej: Aksjomat Martina; promotor: dr B.Grell.
• 1994 doktor nauk matematycznych (Wydział Matematyczno-Fizyczno-Techniczny WSP w Krakowie). Tytuł rozprawy: Równanie Abela na płaszczyźnie i pewne jego zastosowania w teorii iteracji; promotor: prof. dr hab. M. C. Zdun.

Zainteresowania naukowe

Główne kierunki prowadzonych badań:
własności homeomorfizmów Brouwera na płaszczyźnie

Główne wyniki badań:
podanie postaci homeomorfizmów Brouwera zanurzalnych w potok i ich pierwiastków iteracyjnych

Przebieg pracy zawodowej

od 1 X 1988 do chwili obecnej zatrudniony w Instytucie Matematyki Uniwersytetu Pedagogicznego im. Komisji Edukacji Narodowej w Krakowie (wcześniej WSP i AP) - jako pracownik naukowo-dydaktyczny: 1988-1989 asystent stażysta, 1989-1994 asystent, od 1994 adiunkt

Funkcje pełnione w UP

• Kierownik Studiów Podyplomowych w Instytucie Matematyki
• Członek organów kolegialnych Uniwersytetu Pedagogicznego: Rady Wydziału Matematyczno-Fizyczno-Technicznego, Rady Instytutu Matematyki
• Członek Uczelnianej Komisji Wyborczej

Prowadzone (najczęściej) zajęcia dydaktyczne

algebra, geometria, analiza matematyczna, statystyka, ekonometria, matematyka obliczeniowa, matematyczne podstawy informatyki, rozwój pojęć matematycznych, podstawy teoretyczne matematyki szkolnej

Konferencje

Konferencje naukowe:

1. 3rd International Conference on Functional Equations and Inequalities (ICFEI), 03.09.91 - 09.09.91, Koninki, referat: On homeomorphic and diffeomorphic solution of Abel's equation on the plane.
2. European Conference on Iteration Theory (ECIT 92), 13.09.92 - 19.09.92, Batschuns (Austria), referat: Fractional iterates of homeomorphisms of the plane.
3. 4th International Conference on Functional Equations and Inequalities "Stability" (ICFEI), 15.02.93 - 22.02.93, Krynica, referat: On simultaneous Abel inequalities.
4. Polish-Austrian Seminar on Functional Equations and Iteration Theory, 26.10.93 - 31.10.93, Cieszyn, referat: On simultaneous Abel equations on the plane.
5. 32nd International Symposium on Functional Equations (ISFE), 12.06.94 - 19.06.94, Gargnano (Włochy), referat: Homeomorphic solutions of the Abel equation on the plane.
6. European Conference on Iteration Theory (ECIT 94), 28.08.94 - 03.09.94, Opava (Czechy), referat: On continuous iteration groups of homeomorphisms of the plane.
7. 5th International Conference on Functional Equations and Inequalities (ICFEI), 04.09.95 - 09.09.95, Muszyna-Złockie, referat: On three simultaneous Abel equations on the plane
8. 34th International Symposium on Functional Equations (ISFE), 10.06.96 - 19.06.96, Wisła-Jawornik, referat: Continuous iteration groups of free mappings.
9. Topological Methods in Differential Equations and Dynamical Systems (The International Conference organized on the occasion of the 100th anniversary of the birth of Professor Tadeusz Ważewski), 17.07.96 - 19.07.96, Kraków.
10. European Conference on Iteration Theory (ECIT 96), 08.09.96 - 14.09.96, Urbino (Włochy), referat: Continuous iteration groups of free mappings which are homeomorphic.
11. 6th International Conference on Functional Equations and Inequalities (ICFEI), 01.06.97 - 07.06.97, Muszyna-Złockie, referat: On embedding of free mappings in flows.
12. 36th International Symposium on Functional Equations (ISFE), 24.05.98 - 30.05.98, Brno-Bystric (Czechy), referat: A construction of iteration groups of a free mappings.
13. European Conference on Iteration Theory György Targoński in memoriam (ECIT 98), 30.08.98 - 05.09.98, Muszyna-Złockie, referat: Fractional iterations of free mappings.
14. 37-th International Symposium on Functional Equations (ISFE), 16.05.99 - 23.05.99, Huntington (USA), referat: On continuous flows of diffeomorphisms of the plane.
15. 7th International Conference on Functional Equations and Inequalities (ICFEI), 12.09.99 - 18.09.99, Złockie, referat: Iterative roots of homeomorphisms of the plane.
16. 38-th International Symposium on Functional Equations (ISFE), 11.06. - 18.06.2000, Noszvaj (Węgry), referat: On a generalized d'Alembert equation.
17. European Conference on Iteration Theory (ECIT 2000), 04.09. - 09.09.2000, La Manga (Hiszpania), referat: On conjugacy of flows on the plane.
18. 39-th International Symposium on Functional Equations (ISFE), 12.08 - 18.08.2001, Sandbjerg Estate (Dania), referat: On an equivalence relation for flows in the plane.
19. 8th International Conference on Functional Equations and Inequalities (ICFEI), 9.09 - 15.09.2001, Złockie, referat: On the structure of equivalence classes of a relation for a free mapping.
20. 40-th International Symposium on Functional Equations (ISFE), 25.08 - 1.09.2002, Gronów (Polska), referat: On parallelizability of flows of free mappings on the plane.
21. 14th European Conference on Iteration Theory (ECIT 2002), 1.09. - 7.09.2002, Evora (Portugalia), referat: On the structure of equivalence classes of a homeomorphism of the plane.
22. 41-th International Symposium on Functional Equations (ISFE), 8.06. - 15.06.2003, Noszvaj (Węgry), referat: On boundary orbits of a flow of free mappings of the plane.
23. 9th International Conference on Functional Equations and Inequalities (ICFEI), 7.09 - 13.09.2003, Złockie, referat: On boundary and limit orbits of a flow of the plane.
24. 42-nd International Symposium on Functional Equations (ISFE), 20.06-27.06.2004, Hradec nad Moravici (Czechy), referat: On a generalized d'Alembert equation.
25. 15th European Conference on Iteration Theory (ECIT 2004), 29.08. - 4.09.2004, Batschuns (Austria), referat: On boundary orbits of flows.
26. 43-rd International Symposium on Functional Equations (ISFE), 15.05. - 21.05.2005, Batz-sur-Mer (Francja), referat: On a decomposition of the plane for a given flow.
27. 10-th International Conference on Functional Equations and Inequalities (ICFEI), 11.09-17.09.2005, Będlewo, referat: On the d'Alembert equation and its generalization.
28. 44-th International Symposium on Functional Equations (ISFE), 14.05. - 20.05.2006, Louisville KY (USA), referat: On maximal parallelizable regions of a flow of free mappings.
29. 16th European Conference on Iteration Theory (ECIT 2006), 10.09-16.09.2006, Gargnano (Włochy), referat: On the structure of flows of free mappings.
30. 45-th International Symposium on Functional Equations (ISFE), 24.06-1.07.2007, Bielsko-Biała, referat: On boundaries of parallelizable regions of flows of free mappings.
31. Boundary value problems, functional equations and their applications"- Workshop, 16.04-20.04.2008 Kraków, referat: On analytic solutions of the d'Alembert equation.
32. 46-th International Symposium on Functional Equations (ISFE), 22.06-29.06.2008, Opava (Czechy), referat: On Kaplan decompositions for a flow of free mappings.
33. 17th European Conference on Iteration Theory (ECIT 2008), 07.09-13.09.2008, Jałta (Ukraina), referat: On fractional iterates of a free mapping.
34. 47-th International Symposium on Functional Equations (ISFE), 14.06-20.06.2009, Gargnano (Włochy), referat: On the invariance of equivalence classes of the codivergency relation for Brouwer homeomorphisms.
35. 13-th International Conference on Functional Equations and Inequalities (ICFEI), 13.09-19.09.2009 Małe Ciche, referat: On conjugacy of Brouwer homeomorphisms.
36. Boundary value problems, functional equations and their applications 2"- Workshop, 14.04-17.04.2010, Kraków, referat: On Brouwer homeomorphisms of the plane.
37. 48-th International Symposium on Functional Equations (ISFE), 13.06. - 18.06.2010 Batz-sur-Mer (Francja), referat: On one-dimensional foliations of the plane for a Brouwer homeomorphism.
38. 18th European Conference on Iteration Theory (ECIT 2010), 12.09. - 17.09.2010 Nant (Francja), referat: On conjugacy of flows of Brouwer homeomorphisms.
39. 49-th International Symposium on Functional Equations (ISFE), 19.06. - 26.06.2011 Graz-Mariatrost (Austria), referat: On regular points of a Brouwer homeomorphism.
40. 50-th International Symposium on Functional Equations (ISFE), 17.06. - 24.06.2012, Hajdúszoboszló (Węgry), referat: On the structure of Brouwer homeomorphisms embeddable in a flow.
41. 19th European Conference on Iteration Theory (ECIT 2012), 9.09. - 15.09.2012, Ponta Delgada (Portugalia), referat: On foliations of the plane induced by flows of Brouwer homeomorphisms.
42. 15th International Conference on Functional Equations and Inequalities, Ustroń, Polska, 19 - 25 maj, 2013, referat: On approximate solutions of the generalized Volterra integral equation
43. 51st International Symposium on Functional Equations, Rzeszów, Polska, 16 - 23 czerwiec, 2013, referat: On limit sets of Brouwer homeomorphisms embeddable in a flow
44. The 2013 Progress on Difference Equations, Białystok, Polska, 21 - 26 lipiec, 2013, referat: On generating solutions of a third-order equation
45. Conference on Ulam's Type Stability, Rytro, Polska, 2 - 6 czerwiec, 2014, referat: On stability of an operator type equation of order n
46. 52nd International Symposium on Functional Equations, Innsbruck, Austria, 22 - 29 czerwiec, 2014, referat: On properties of generalized Reeb flows
47. Fourth Small Workshop on Operator Theory , Kraków, Polska, 8 - 11 lipiec, 2014, referat: On generating solutions of a generalized Volterra integral equation
48. 20th European Conference on Iteration Theory, Łagów, Polska, 14 - 20 wrzesień, 2014, referat: On strongly irregular points of a Brouwer homeomorphism embeddable in a flow
49. 16th International Conference on Functional Equations and Inequalities, Będlewo, Polska, 17 - 23 maj, 2015, referat: On the topological equivalence of flows of Brouwer homeomorphisms
50. 53rd International Symposium on Functional Equations, Krynica-Zdrój, Polska, 14 - 21 czerwiec, 2015, referat: On the topological conjugacy of flows of generalized Reeb homeomorphisms
51. The 21st International Conference on Difference Equations and Applications 2015, Białystok, Polska, 19 - 24 lipiec, 2015, referat: On topological properties of flows of Brouwer homeomorphisms
52. 54th International Symposium on Functional Equations, Hajdúszoboszló, Węgry, 12 - 19 czerwiec, 2016, referat: On the topological conjugacy of flows of Brouwer homeomorphisms
53. Conference on Ulam's Type Stability, Cluj-Napoca, Rumunia, 4 - 9 lipiec, 2016, referat: On the stability of a generalized Fréchet functional equation with constant coefficients
54. The 22nd International Conference on Difference Equations and Applications 2016, Osaka, Japonia, 24 - 29 lipiec, 2016, referat: On topological invariants of Brouwer flows
55. 21st European Conference on Iteration Theory, Innsbruck, Austria, 4 - 10 wrzesień, 2016, referat: On properties of the set of regular points of a Brouwer homeomorphisms
56. Progress on Difference Equations 2017, Urbino, Włochy, 29 - 31 maj, 2017, referat: On topological properties of Brouwer homeomorphisms
57. 55th International Symposium on Functional Equations, Chengdu, Chiny, 11 - 18 czerwiec, 2017, referat: On properties of the set of invariant lines of a Brouwer homeomorphism
58. 17th International Conference on Functional Equations and Inequalities, Będlewo, Polska, 9 - 15 lipiec, 2017, referat: On properties of Brouwer flows and Brouwer homeomorphisms
59. Dynamical Systems, Difference and Functional Equations. In honor of Marek C. Zdun's 70th birthday, Krynica Zdrój, Polska, 4 - 8 czerwiec, 2018, referat: From solutions of bounded variations of the linear functional equation to iteration semigroups and groups - selected results of Marek C. Zdun
60. 56th International Symposium on Functional Equations, Graz-Mariatrost, Austria, 17 - 24 czerwiec, 2018, referat: On the boundaries of equivalence classes of the codivergency relation for Brouwer homeomorphisms
61. European Conference on Iteration Theory 2018, Murcia, Hiszpania, 3 - 6 lipiec, 2018, referat: On translation lines for Brouwer homeomorphisms
62. Conference on Ulam's Type Stability, Timișoara, Rumunia, 8 - 13 październik, 2018, referat: Fixed points of a linear operator of polynomial form
63. Progress on Difference Equations 2019, Bragança, Portugalia, 27 - 30 maj, 2019, referat: On families of invariant lines of a Brouwer homeomorphism
64. 57th International Symposium on Functional Equations, Jastarnia, Polska, 2 - 9 czerwiec, 2019, referat: On foliations of the plane induced by Brouwer homeomorphisms
65. 18th International Conference on Functional Equations and Inequalities, Będlewo, Polska, 9 - 15 czerwiec, 2019, referat: On fixed points of functions with values in a dq-metric space
66. Dynamics, Equations and Applications 2019, Kraków, Polska, 16 - 20 wrzesień, 2019, referat: On fractional iterates of a Brouwer homeomorphism
67. 26th International Conference on Difference Equations and Applications, Sarajevo, Bośnia i Hercegowina, 26 - 30 lipiec, 2021, referat: On continuity of fractional iterates of Brouwer homeomorphisms
68. 19th International Conference on Functional Equations and Inequalities, Będlewo, Polska, 12 - 18 wrzesień, 2021, referat: On a construction of iterative roots of a Brouwer homeomorphism
69. 27th International Conference on Difference Equations and Applications, Paris, Francja, 18 - 22 lipiec, 2022, referat: On extension of fractional iterates of a Brouwer homeomorphism from a parallelizable region
70. 4th International Workshop on Nonlinear Analysis and its Applications, Sapanca, Turcja, 12 - 15 październik, 2022, referat: On a matching property for invariant lines of a Brouwer homeomorphism
71. 59th International Symposium on Functional Equations, Hajdúszoboszló, Węgry, 18 - 25 czerwiec, 2023, referat: On iterative roots of a Brouwer homeomorphism generating foliations of the plane
72. 28th International Conference on Difference Equations and Applications, Phitsanulok, Tajlandia, 17 - 21 lipiec, 2023, referat: On Brouwer homeomorphisms generating foliations of the plane
73. 20th International Conference on Functional Equations and Inequalities, Będlewo, Polska, 17 - 23 wrzesień, 2023, referat: On foliations consisting of invariant lines of a Brouwer homeomorphism
74. 60th International Symposium on Functional Equations, Kościelisko, Polska, 9 - 15 czerwiec, 2024, referat: On iterative roots of a Brouwer homeomorphism having a matching property
75. 29th International Conference on Difference Equations and Applications, Paryż, Francja, 24 - 28 czerwiec, 2024, referat: On limit sets of Brouwer homeomorphisms generating foliations of the plane

Członkostwo w organizacjach i komitetach naukowych, redakcjach czasopism, itp.

• Polskie Towarzystwo Matematyczne PTM - członek

Nagrody, wyróżnienia, odznaczenia

Odznaczenia Państwowe:


2003 Brązowy Krzyż Zasługi

2015 Medal Komisji Edukacji Narodowej

Nagrody Rektora WSP/AP/UP:


Nagrody Rektora: 1994, 2006

Wyróżnienia naukowe:
Nagrody w ogólnopolskim konkursie na najlepszą polską pracę z równań funkcyjnych i zagadnień pokrewnych im Marka Kuczmy organizowanym przez Uniwersytet Śląski w Katowicach
- 1993 II nagroda za pracę On homeomorphic and diffeomorphic solutions of the Abel equation on the plane, Ann. Polon. Math. 58 (1993), 7--18.
- 2002 III nagroda za pracę On fractional iterates of a homeomorphism of the plane, Ann. Polon. Math. 79 (2002), 129--137.
- 2010 II nagroda za pracę On fractional iterates of a free mapping embeddable in a flow, J. Math. Anal. Appl. 366 (2010), 310-318.

Publikacje

Artykuły naukowe:

1. I. Aboutaib, C. Benzarouala, J. Brzdęk, Z. Leśniak, L. Oubbi, Ulam stability of a general linear functional equation in modular spaces, Symmetry 14 (2022), ID: 2468: 12 pp.
2. J. Brzdęk, Z. Leśniak, R. Malejki, On the stability of a generalized Fréchet functional equation with respect to hyperplanes in the parameter space, Symmetry 13 (2021), ID: 384: 21 pp.
3. A. Bahyrycz, J. Brzdęk, El-s. El-hady, Z. Leśniak, On Ulam stability of functional equations in 2-normed spaces - a survey, Symmetry 13 (2021), ID: 2200: 19 pp.
4. J. Brzdęk, A. Fošner, Z. Leśniak, A note on asymptotically approximate generalized Lie derivations, J. Fixed Point Theory Appl. 22 (2020), Article:40: 13
5. Z. Leśniak, On the topological conjugacy of Brouwer flows, Bull. Malays. Math. Sci. Soc. 42 (2019), 1639-1655
6. Z. Leśniak, On families of invariant lines of a Brouwer homeomorphism, J. Difference Equ. Appl. 25 (2019), 1363-1371
7. Z. Leśniak, On properties of the set of invariant lines of a Brouwer homeomorphism, J. Difference Equ. Appl. 24 (2018), 746-752
8. J. Brzdęk, Z. Leśniak, R. Malejki, On the generalized Fréchet functional equation with constant coefficients and its stability, Aequationes Math. 92 (2018), 355-373
9. J. Brzdęk, El-s. El-hady, Z. Leśniak, On fixed points of a linear operator of polynomial form of order 3, J. Fixed Point Theory Appl. 20 (2018), Article:85: 10
10. J. Brzdęk, El-s. El-hady, Z. Leśniak, Fixed-point theorem in classes of function with values in a dq-metric space, J. Fixed Point Theory Appl. 20 (2018), Article:143: 16
11. Z. Leśniak, On the topological equivalence of flows of Brouwer homeomorphisms, J. Difference Equ. Appl. 22 (2016), 853-864
12. J. Brzdęk, El-s. El-hady, W. Förg-Rob, Z. Leśniak, A note on solutions of a functional equation arising in a queueing model for a LAN gateway, Aequationes Math. 90 (2016), 671-681
13. J. Brzdęk, L. Cădariu, K. Ciepliński, A. Fošner, Z. Leśniak, Survey on recent Ulam stability results concerning derivations, J. Funct. Spaces 2016, Article ID 1235103: 9
14. Z. Leśniak, Y.-G. Shi, Topological conjugacy of piecewise monotonic functions of nonmonotonicity height ≥1 , J. Math. Anal. Appl. 423 (2015), 1792 -1803
15. A. Bahyrycz, J. Brzdęk, Z. Leśniak, On approximate solutions of the generalized Volterra integral equation, Nonlinear Anal. Real World Appl. 20 (2014), 59-66
16. Z. Leśniak, On Strongly Irregular Points of a Brouwer Homeomorphism Embeddable in a Flow, Abstr. Appl. Anal. 2014, Article ID 638784: 7
17. J. Brzdęk, K. Ciepliński, Z. Leśniak, On Ulam's type stability of the linear equation and related issues, Discrete Dyn. Nat. Soc. 2014, Art. ID 536791: 14 pp.
18. K. Ciepliński, Z. Leśniak, On conjugacy equation in dimension one, Banach Center Publ. 99 (2013), 31-44
19. Y.-G. Shi, Lin Li, Z. Leśniak, On conjugacy of r-modal interval maps with non-monotonicity height equal to 1, J. Difference Equ. Appl. 19 (2013), 573-584
20. Z. Leśniak, On the structure of Brouwer homeomorphisms embeddable in a flow, Abstr. Appl. Anal., vol. 2012 (2012), Article ID 248413, 8 str.
21. Z. Leśniak, Yong-Guo Shi, One class of planar rational involutions, Nonlinear Anal. 74 (2011), No. 17, 6097-6104.
22. Z. Leśniak, On fractional iterates of a free mapping embeddable in a flow, J. Math. Anal. Appl. 366 (2010), 310-318.
23. Z. Leśniak, On a decomposition of the plane for a flow of free mappings, Publ. Math. Debrecen 75 (2009), No. 1-2, 191-202.
24. Z. Leśniak, On the existence of analytic solutions of the d'Alembert equation, Int. J. Pure Appl. Math. 48 (2008), No. 3, 385-397.
25. Z. Leśniak, On the first prolongational limit set of flows of free mappings, Tamkang J. Math. 39, No 3 (2008), 263-269.
26. Z. Leśniak, On boundary orbits of a flow of free mappings of the plane, Int. J. Pure Appl. Math. 42 (2008), No. 1, 5-11.
27. Z. Leśniak, On boundaries of parallelizable regions of flows of free mappings, Abstr. Appl. Anal., vol. 2007, Article ID 31693, 8 str. (2007).
28. Z. Leśniak, On maximal parallelizable regions of flows of the plane, Int. J. Pure Appl. Math. 30 (2006), No. 2, 151-156.
29. Z. Leśniak, On parallelizable regions of flows of the plane, Grazer Math. Ber. 350 (2006), 175-183.
30. Z. Leśniak, On parallelizability of flows of free mappings, Aequationes Math. 71 (2006), No. 3, 280-287.
31. Z. Leśniak, On an equivalence relation for free mappings embeddeable in a flow, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 17 (2003), No 7, 1911-1915.
32. Z. Leśniak, On fractional iterates of a homeomorphism of the plane, Ann. Polon. Math. 79 (2002), No.2, 129-137.
33. Z. Leśniak, On continuous iteration groups of some homeomorphisms of the plane, Grazer Math. Ber. 334 (1997), 193-198.
34. Z. Leśniak, Constructions of fractional iterates of Sperner homeomorphisms of the plane, Förg-Rob, W. (ed.) et al., Iteration theory. Proceedings of the European conference, ECIT '92, Batschuns, Austria, September 13--19, 1992. Singapore: World Scientific. 182-192 (1996).
35. Z. Leśniak, On the system of the Abel equations on the plane, Ann. Math. Sil. 9 (1995), 105-122.
36. M.C. Zdun, Z. Leśniak, On iteration groups of singularity-free homeomorphisms of the plane, Ann. Math. Sil. 8 (1994), 203-210.
37. Z. Leśniak, On simultaneous Abel inequalities, Opuscula Math. 14 (1994), 107-115.
38. Z. Leśniak, On homeomorphic and diffeomorphic solutions of the Abel equation on the plane, Ann. Polon. Math. 58 (1993), No 1, 7-18.

Rozprawy:

39. Równanie Abela na płaszczyźnie i pewne jego zastosowania w teorii iteracji (maszynopis), praca doktorska pod kierunkiem Prof. dr. hab. M. C. Zduna, WSP Kraków, 1993.