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Instytut Matematyki
Logo Europejskie Miasto Nauki Katowice 2024
home link Pracownicy prof. dr hab. Karol Baron

prof. dr hab. Karol Baron

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 Profesor

Pracownicy badawczo-dydaktyczni

Analiza Rzeczywista

581

(32) 359 14 35

karol.baron@us.edu.pl

0000-0002-0807-2776

 
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Wykształcenie

  • Magisterium: Uniwersytet Śląski, matematyka, 29 VI 1971
  • Doktorat: Uniwersytet Śląski; Wydział Matematyki, Fizyki i Chemii; 16 I 1974
    (promotor: prof. zw. dr hab. Marek Kuczma)
  • Habilitacja: Uniwersytet Śląski; Wydział Matematyki, Fizyki i Chemii; 7 X 1980
  • Profesura: tytuł naukowy profesor nauk matematycznych, nadany przez Prezydenta Rzeczypospolitej Polskiej 15 I 1996

Funkcje pełnione w latach ubiegłych

  • wicedyrektor Instytutu Matematyki (1 IX 1981 – 31 VIII 1987)
  • dyrektor Instytutu Matematyki (1 IX 1987 – 29 II 1992)
  • kierownik Zakładu Analizy Rzeczywistej (1 IX 1987 – 30 VI 2014)
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Publikacje Publikacje

Artykuły naukowe

  1. On some generalization of the Pexider equation, Univerzitet u Beogradu. Publikacije Elektrotehnickog Fakulteta. Serija Matematika i Fizika No. 330-337 (1970), 35-38.
  2. (jointly with J. Matkowski) On the solutions fulfilling a Lipschitz condition of a nonlinear functional equation of order n, Revue Roumaine de Mathématiques Pures et Appliquées 17 (1972), 1149-1154.
  3. (jointly with J. Matkowski) A fixed point theorem for non-expansive mappings on compact metric spaces, Institut Mathématique. Publications. Nouvelle Série (Belgrade) 15 (29) (1973), 25-26.
  4. On the continuous solutions of a non-linear functional equation of the first order, Annales Polonici Mathematici 28 (1973), 201-205.
  5. Continuous solutions of a functional equation of n-th order, Aequationes Mathematicae 9 (1973), 257-259.
  6. (jointly with R. Ger) On Mikusinski-Pexider functional equation, Colloquium Mathematicum 28 (1973), 307-312.
  7. On the continuous dependence of continuous solutions of a functional equation of n-th order on given functions, Aequationes Mathematicae 10 (1974), 78-80.
  8. Note on the existence of continuous solutions of a functional equation of n-th order, Annales Polonici Mathematici 30 (1974), 77-80.
  9. A few observations regarding continuous solutions of a system of functional equations, Publicationes Mathematicae (Debrecen) 21 (1974), 185-191.
  10. Note on continuous solutions of a functional equation, Aequationes Mathematicae 11 (1974), 267-269.
  11. (jointly with R. Ger and J. Matkowski) Analytic solutions of a system of functional equations, Publicationes Mathematicae (Debrecen) 22 (1975), 189-194.
  12. On approximate solutions of a functional equation, Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques 23 (1975), 1065-1068.
  13. On extending solutions of a functional equation, Aequationes Mathematicae 13 (1975), 285-288.
  14. (jointly with R. Ger) An integral version of some theorems occuring in the theory of functional equations, Mathematica (Cluj) 17 (40) (1975), 5-10.
  15. (jointly with R. Ger) Lyapunov stability of continuous solutions of some functional equations,
    Analele Stiintifice ale Universitatii „Al. I. Cuza” din Iasi. Seria Noua. Sectinea I a Matematica 22 (1976), 165-172.
  16. (jointly with J. Matkowski) On sequences of contraction mappings, Revue Roumaine de Mathématiques Pures et Appliquées 22 (1977), 1041-1043.
  17. (jointly with M. Kuczma) Iteration of random-valued functions on the unit interval, Colloquium Mathematicum 37 (1977), 263-269.
  18. (jointly with M. Sablik) On the uniqueness of continuous solutions of a functional equation of n-th order, Aequationes Mathematicae 17 (1978), 295-304.
  19. Functional equations of infinite order, Prace Naukowe Uniwersytetu Slaskiego w Katowicach Nr 265. Uniwersytet Slaski 1978.
  20. Note on measures, Mathematica Slovaca 28 (1978), 379-383.
  21. On approximate solutions of a system of functional equations, Annales Polonici Mathematici 43 (1983), 305-316.
  22. On integrable solutions of some functional equations, La Société Royale du Canada. L’Academie des Sciences. Comptes Rendus Mathématiques 5 (1983), 265-267.
  23. (jointly with W. Jarczyk) On approximate solutions of functional equations of countable order, Aequationes Mathematicae 28 (1985), 22-34.
  24. A remark on linear functional equations in the indeterminate case, Glasnik Matematicki 20 (40) (1985), 373-376.
  25. A remark on the stability of the Cauchy equation, Rocznik Naukowo-Dydaktyczny Wyzszej Szkoły Pedagogicznej w Krakowie. Prace Matematyczne 11 (1985), 7-12.
  26. (jointly with J. Walorski) P235S1, Aequationes Mathematicae 32 (1987), 153.
  27. On the convergence of sequences of iterates of random-valued functions, Aequationes Mathematicae 32 (1987), 240-251.
  28. (jointly with W. Jarczyk) On a way of division of segments, Aequationes Mathematicae 34 (1987), 195-205.
  29. P283R2, Aequationes Mathematicae 35 (1988), 301-303.
  30. (jointly with P. Volkmann) On the Cauchy equation modulo Ζ, Fundamenta Mathematicae 131 (1988), 143-148.
  31. On a problem of R. Schilling, Berichte der mathematisch-statistischen Sektion in der Forschungsgesellschaft Joanneum – Graz 286 (1988).
  32. On the continuous solutions of the Gołąb-Schinzel equation, Aequationes Mathematicae 38 (1989), 155-162.
  33. (jointly with PL. Kannappan) On the Pexider difference, Fundamenta Mathematicae 134 (1990), 247-254.
  34. On a problem of Z. Daróczy, Zeszyty Naukowe Politechniki Śląskiej. Matematyka-Fizyka 64 (1990), 51-54.
  35. (jointly with P. Volkmann) On a Theorem of van der Corput, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 61 (1991), 189-195.
  36. M. Kuczma’s papers on iterative functional equations, Grazer Mathematische Berichte 316 (1992), 1-6.
  37. (jointly with P. Volkmann) Unicité pour une équation fonctionnelle, Rocznik Naukowo-Dydaktyczny Wyzszej Szkoły Pedagogicznej w Krakowie. Prace Matematyczne 13 (1993), 53-56.
  38. (jointly with J. Rätz) Orthogonality and additivity modulo a subgroup, Aequationes Mathematicae 46 (1993), 11-18.
  39. (jointly with PL. Kannappan) On the Cauchy difference, Aequationes Mathematicae 46 (1993), 112-118.
  40. (jointly with A. Lasota) Asymptotic properties of Markov operators defined by Volterra type integrals, Annales Polonici Mathematici 58 (1993), 161-175. (Short communication: Grazer Mathematische Berichte 316 (1992), 213-218).
  41. (jointly with J. Matkowski and K. Nikodem) A sandwich with convexity, Mathematica Pannonica 5 (1994), 139-144.
  42. (jointly with H. Hudzik) Orlicz spaces which are L℘-spaces, Aequationes Mathematicae 48 (1994), 254-261.
  43. (jointly with A. Simon) On approximate solutions of an iterative functional equation, Annales Mathematicae Silesianae 8 (1994), 79-84.
  44. (jointly with G.L. Forti) Orthogonality and additivity modulo ℤ, Results in Mathematics 26 (1994), 205-210.
  45. (jointly with A. Simon and P. Volkmann) Solutions d’une équation fonctionnelle dans l’espace des distributions tempérées, Comptes Rendus des Séances de l’Académie des Sciences. Série I. Mathématiques. (Paris) 319 (1994), 1249-1252.
  46. (jointly with F. Halter-Koch and P. Volkmann) On orthogonally exponential functions, Archiv der Mathematik 64 (1995), 410-414.
  47. (jointly with J. Rätz) On orthogonally additive mappings on inner product spaces, Bulletin of the Polish Academy of Sciences. Mathematics 43 (1995), 187-189.
  48. (jointly with A. Simon and P. Volkmann) On functions having Cauchy differences in some prescribed sets, Aequationes Mathematicae 52 (1996), 254-259.
  49. (jointly with P. Volkmann) On orthogonally additive functions, Publicationes Mathematicae (Debrecen) 52 (1998), 291-297. 
  50. (jointly with A. Kucia) On regularity of functions connected with orthogonal additivity, Functiones et Approximatio Commentari Mathematici 26 (1998), 19-24. 
  51. (jointly with A. Lasota) Markov operators on the space of vector measures; coloured fractals, Annales Polonici Mathematici 69 (1998), 217-234. 
  52. Appendix to the chapter Synthesis of the Firing of Many Neurons of The Brain: Unraveling the Mystery of How it Works by T. L. Saaty, RWS Publications, Pittsburgh 2000; pp. 339-347. 
  53. (jointly with M. Sablik and P. Volkmann) On decent solutions of a functional congruence, Rocznik Naukowo-Dydaktyczny Akademii Pedagogicznej w Krakowie. Prace Matematyczne 17 (2000), 27-40. 
  54. (jointly with W. Jarczyk) Recent results on functional equations in a single variable, perspectives and open problems, Aequationes Mathematicae 61 (2001), 1-48. 
  55. On the continuity of additive-like functions and Jensen convex functions which are Borel on a sphere, Functional Equations – Results and Advances, Edited by Z. Daróczy and Z. Páles, Kluwer Academic Publishers 2002, 17-20. 
  56. (jointly with P. Volkmann) On functions close to homomorphisms between square symmetric structures, Seminar LV, No. 14, 12 pp. (2002) (DOI: 10.5445/IR/8582002). 
  57. Recent results in the theory of functional equations in a single variable, Seminar LV, No. 15, 16 pp. (2003) (DOI: 10.5445/IR/62003). 
  58. (jointly with P. Volkmann) Dense sets of additive functions, Seminar LV, No. 16, 4 pp. (2003) (DOI: 10.5445/IR/1322003).
  59. (jointly with Z. Kominek) On functionals with the Cauchy difference bounded by a
    homogeneous functional    , Bulletin of the Polish Academy of Sciences. Mathematics 51 (2003), 301-307.
  60. (jointly with W. Jarczyk) Random-valued functions and iterative functional equations, Aequationes Mathematicae 67 (2004), 140-153. 
  61. (jointly with W. Jarczyk) Improving regularity of some functions by Grosse-Erdmann’s theorems, Grazer Mathematische Berichte 346 (2004), 37-42. 
  62. (jointly with H.-H. Kairies) Characterizations of eigenspaces by functional equations, Aequationes Mathematicae 68 (2004), 248-259. 
  63. Powers of topological group characters and a theorem of van der Corput, Annales Societatis Mathematicae Polonae. Series I: Commentationes Mathematicae. Tomus Specialis in honorem Iuliani Musielak (2004), 65-69. 
  64. (jointly with W. Jarczyk) On continuity of solutions to some equations of iteration theory, Aequationes Mathematicae 69 (2005), 28-31. 
  65. (jointly with P. Volkmann) Characterization of quasimonotonicity by means of functional inequalities, Seminar LV, No. 22, 5 pp. (2005) (DOI: 10.5445/IR/1000003621). 
  66. Orthogonality and additivity modulo a discrete subgroup, Aequationes Mathematicae 70 (2005), 189-190. 
  67. (jointly with W. Jarczyk) Non-negative solutions of a convolution equation, La Société Royale du Canada. L’Academie des Sciences. Comptes Rendus Mathématiques 28 (2006), 1-5. 
  68. (jointly with P. Volkmann) Characterization of the absolute value of complex linear functionals by functional equations, Seminar LV, No. 28, 10 pp. (2006) (DOI: 10.5445/IR/1000007406). 
  69. (jointly with W. Chojnacki and W. Jarczyk) Continuity of solutions of the translation equation, Aequationes Mathematicae 74 (2007), 314-317. 
  70. (jointly with z R. Kapica) A uniqueness-type problem for linear iterative equations, Analysis (Munich) 29 (2009), 95-101. 
  71. Linear iterative equations of higher orders and random-valued functions, Publicationes Mathematicae (Debrecen) 75 (2009), 1-9. 
  72. On the convergence in law of iterates of random-valued functions, The Australian Journal of Mathematical Analysis and Applications 6 (2009), no. 1, Art. 3, 9 pp. 
  73. On Baire measurable solutions of some functional equations, Central European Journal of Mathematics 7 (2009), 804-808. 
  74. On continuous involutions and Hamel bases, Annales Mathematicae Silesianae 25 (2011), 45-48. 
  75. Marek Kuczma, Recent Developments in Functional Equations and Inequalities, Banach Center Publications 99 (2013), 9-16, Polish Academy of Sciences, Institute of Mathematics, Warszawa. 
  76. On some orthogonally additive functions on inner product spaces, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica 40 (2013), 123-127. 
  77. On orthogonally additive functions with orthogonally additive second iterate, Commentationes Mathematicae 53 (2013), 401-404. 
  78. On additive involutions and Hamel bases, Aequationes Mathematicae 87 (2014), 159-163. 
  79. Orthogonally additive bijections are additive, Aequationes Mathematicae 89 (2015), 297-299. 
  80. On the continuous dependence of solutions to orthogonal additivity problem on given functions, Annales Mathematicae Silesianae 29 (2015), 19-23. 
  81. On the continuous dependence in a problem of convergence of iterates of random-valued functions, Grazer Mathematische Berichte 363 (2015), 1-6. 
  82. On orthogonally additive injections and surjections, Commentationes Mathematicae 55 (2015), 157-162. 
  83. (jointly with R. Kapica and J. Morawiec) On Lipschitzian solutions to an inhomogeneous linear iterative equation, Aequationes Mathematicae 90 (2016), 77-85. 
  84. (jointly with J. Morawiec) Lipschitzian solutions to linear iterative equations, Publicationes Mathematicae (Debrecen) 89 (2016), 277-285. 
  85. (jointly with J. Morawiec) Lipschitzian solutions to linear iterative equations revisited, Aequationes Mathematicae 91 (2017), 161-167. 
  86. On orthogonally additive functions with big graphs, Annales Mathematicae Silesianae 31 (2017), 57-62. 
  87. On the set of orthogonally additive functions with orthogonally additive second iterate, Aequationes Mathematicae 91 (2017), 995-1000. 
  88. Weak law of large numbers for iterates of random-valued functions, Aequationes Mathematicae 93 (2019), 415-423. 
  89. Weak limit of iterates of some random-valued functions and its application, Aequationes Mathematicae 94 (2020), 415-425; 427 (Correction). 
  90. Remarks connected with the weak limit of iterates of some random-valued functions and iterative functional equations, Annales Mathematicae Silesianae 34 (2020), 36-44 (doi: 10.2478/amsil-2019-0015).
  91. Around the weak limit of iterates of some random-valued functions, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, Sectio Computatorica 51 (2020), 31-37 (link).
  92. Continuous solutions to two iterative functional equations, Aequationes Mathematicae 95 (2021), 1157-1168 (doi: 10.1007/s00010-021-00794-x).
  93. (jointly with J. Wesołowski) From invariance under binomial thinning to unification of the Cauchy and the Gołąb–Schinzel–type equations, Results in Mathematics 76, 168 (2021) (doi: 10.1007/s00025-021-01457-8).
  94. (jointly with Rafał Kapica) Strong law of large numbers for iterates of some random-valued functions, Results in Mathematics 77 (2022), 50 (doi: 10.1007/s00025-021-01586-0).
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