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prof. dr hab. Kazimierz Nikodem

Portret

Curriculum Vitae

  1. Degrees:
    • M.Sc. in Mathematics, 1977, Silesian University, Katowice;
    • Ph.D. in Mathematics, 1981, Silesian University, Katowice;
    • Habilitation in Mathematics, 1991, Polish Academy of Sciences, Warsaw;
    • Title of Professor , 2001, Warsaw.
  2. Employment:
    • 1977 - 1981 : Assistant, Silesian University, Katowice
    • 1981 - 1984 : Assistant Professor (Adiunkt), Silesian University, Katowice
    • 1984 - 1991 : Assistant Professor (Adiunkt), Technical University of Łódź, Branch in Bielsko-Biała
    • 1991 - 2003 : Associate Professor, Technical Univ.of Łódź, Branch in Bielsko-Biała, since 2001 - University of Bielsko-Biała
    • 2003 - : Full Professor, University of Bielsko-Biała
  3. Functions:
    • Head of the Department of Mathematics and Computer Science (since 1997)
    • Dean of the Faculty of Mechanical Engineering and Computer Science (1999-2005)
    • Vice-Rector of Research and General Affairs (2006-2008)
    • Vice-Rector of Science and Finance (2012 - 2016)
  4. Research fields:
    • Convex analysis
    • functional equations and inequalities
    • set-valued functions
  5. Professional experience:
    • over 100 publications in mathematical journals in Canada, Croatia, Austria, France, Germany, USA, Japan, Italy, Romania, Switzerland, Hungary, Netherlands and Poland;
    • talks on over 100 international conferences in Polana and abroad ( Austria, Brasil, Canada, China, Croatia, Czech Republic, Denmark, France, Germany, Great Britain, Hungary, India, Italy, Iran, Romania, Slovakia, Spain, Sweden, Taiwan, USA, Yugoslavia);
    • visiting professor at the universities in: Waterloo (1988), Perugia (1992,1993), Caracas (1996, 2006, 2010, 2011, 2013, 2014, 2015), Sankt Petersburg (1997), Debrecen (1997, 2002, 2005, 2008, 2010, 2013, 2014), Split (2015, 2016, 2017), Innsbruck (1998), Cluj-Napoca (2000, 2019), Chengdu (2000, 2006, 2015, 2017), Oradea (2005), Louisville (2006), Hong Kong (2006), Merida (2011), Chongquing (2015), Neijiang (2015), Melbourne (2016), Tokio-Chiba (2016), Jiaxing (2018), Hanoi-VIASM (2018);
    • reviewer for Mathematical Reviews and Zentralblatt für Mathematik.
  6. Supervisor of 4 Ph.D. dissertations:
    • Szymon Wąsowicz (1997),
    • Elżbieta Sadowska-Owczorz (1999),
    • Mirosław Adamek (2005),
    • Dawid Kotrys (2016)
  7. Professional memberships:
    • Polish Association of Mathematicians (since 1978)
    • American Mathematical Society (since 1984)
  8. Teaching experience:
    • Lectures on mathematical analysis, algebra, differential equations,calculus of probability
    • Lectures on mathematics for engineering and management students.
  9. Publications:
    • Ph.D. Dissertation: Wypukłe i kwadratowe procesy stochastyczne , Uniwersytet Śląski, Katowice, 1981.
    • Habilitation Dissertation: K-convex and K-concave set-valued functions, Zeszyty Nauk.Politech.Łódz.Mat. 559 (Rozprawy Nauk. 114), Łódź 1989, pp. 1-75.
    • List of publications:
      1. K. Nikodem, On convex stochastic processes, Aequationes Math. 20 (1980), 184-197.
      2. K. Nikodem, On quadratic stocastic processes, Aequationes Math. 21 (1980), 192-199.
      3. K. Nikodem, Some remarks on quadratic stochastic processes, Prace Nauk.Uniw.Śląsk. Katowic. 11 (1981), 21-25.
      4. K. Nikodem, On additive set-valued functions, Rev.Roumaine Math.Pures Appl. 26 (1981), 1005-1013.
      5. K. Nikodem, Additive set-valued functions in Hilbert spaces, Rev.Roumaine Math. Pures Appl. 28 (1983), 239-242.
      6. K. Nikodem, On quadratic set-valued functions, Publ.Math.Debrecen 30 (1983), 297-301.
      7. K. Nikodem, Continuity of K-convex set-valued functions, Bull.Acad.Polon.Sci.Ser.Sci. Math. 34 (1986), 393-400.
      8. K. Nikodem, Midpoint convex functions majorized by midpoint concave functions, Aequationes Math. 32 (1987), 45-51.
      9. K. Nikodem, On midpoint convex set-valued functions, Aequationes Math. 33 (1987), 46-56.
      10. K. Nikodem, On Jensen's functional equation for set-valued functions, Radovi Mat. 3 (1987), 23-33.
      11. K. Nikodem, On concave and midpoint concave set-valued functions, Glas.Mat.Ser.III 22 (1987), 69-76.
      12. K. Nikodem, Set-valued solutions of the Pexider functional equation, Funkcial Ekvac. 31 (1988), 227-231.
      13. K. Nikodem, Approximately quasiconvex functions, C.R.Math.Rep.Acad.Sci.Canada 10 (1988), 291-294.
      14. K. Nikodem, Extreme points and linear transformatios, Mathematica (Cluj) 30 (1988), 157-159.
      15. K. Nikodem, Additive selections of additive set-valued functions, Zb.Rad.Prirod.Mat. Fak. Univ. u Novom Sadu 18 (1988), 143-148.
      16. K. Nikodem, On some class of midconvex functions, Ann.Polon.Math. 50 (1989), 145-151.
      17. K. Nikodem, A characterization of midconvex set-valued functions, Acta Univ.Carolin.- Math.Phys. 30 (1989), 125-129.
      18. K. Nikodem, On some properties of quadratic stochastic processes, Ann.Math.Silesianae 3 (1990), 58-69.
      19. K. Nikodem, Remarks on K-midconvex set-valued functions with closed epigraph, Le Mathematiche 45 (1990), 277-281.
      20. K. Nikodem, The stability of Pexider functional equation, Ann.Math.Silesianae 5 (1991), 91-93.
      21. K. Nikodem, On the support of midconvex operators, Aequationes Math. 42 (1991), 182-189.
      22. K. Nikodem, On e-invariant measures and a functional equation, Czechoslovak Math.J. 41 (1991), 565-569.
      23. Gy. Maksa, K. Nikodem and Zs. Páles, Results on t-Wright convexity, C.R.Math.Rep.Acad.Sci.Canada 13 (1991), 274-278.
      24. N. Merentes and K. Nikodem, On Nemytskii operator and set-valued functions of bounded p-variation, Radowi Math. 8 (1992), 139-145.
      25. K. Nikodem and C. T. Ng, Approximately midconvex functions, Canada, Proc.Amer.Math.Soc. 118 (1993), 103-108.
      26. J. Matkowski and K. Nikodem, Solutions of some functional inequalities connected with convex functions, C.R.Math.Sci.Canada 15 (1993), 114-118.
      27. T. Cardinali and K. Nikodem, F. Papalini, Some results on stability and on characterization of K-convexity of set-valued functions, Ann.Polon.Math. 58 (1993), 185-192.
      28. K. Baron, J. Matkowski and K. Nikodem, A sandwich with convexity, Mathematica Pannonica 5/1 (1994), 139-144.
      29. A. Fiakka, K. Nikodem and F. Papalini, Hull-concave set-valued functions, Ann.Math.Silesianae 8 (1994), 211-216.
      30. J. Matkowski and K. Nikodem, An integral Jensen inequality for convex multifunctions, Results in Mathematics 26 (1994), 349-353.
      31. K. Nikodem and Sz. Wąsowicz, A sandwich theorem and Hyers-Ulam stability af affine functions, Aequationes Math 49 (1995), 160-164.
      32. E. Behrends and K. Nikodem, A selection theorem of Helly type and its applications, Studia Math. 116 (1995), 43-48.
      33. W. Forg-Rob, K. Nikodem and Zs. Páles, Separation by monotonic functions, Mathematica Pannonica 7 (1996), 191-196.
      34. N. Merentes, K. Nikodem and S. Rivas, Continuity of the superposition of set-valued function, Journal of Applied Analysis 3 (1997),43-48.
      35. K. Nikodem, F. Papalini and S. Vercillo, Some representations of midconvex set-valued functions, Aequationes Math.53 (1997), 127-140.
      36. K. Nikodem and Zs. Páles, A characterization of midpoint quasiaffine functions, Publ. Math.Debrecen 52 (3-4) (1998), 575-595.
      37. J. Matkowski and K. Nikodem, Convex set-valued functions on (0,inf) and their conjugate, Rocznik Nauk.-Dydakt. WSP w Krakowie 196, Prace Mat.15 (1998),103-107.
      38. K. Nikodem, Zs. Páles and Sz. Wąsowicz, Abstract separation theorems of Rode type and their applications, Ann.Polon.Math.72(3) (1999), 207-217.
      39. K. Nikodem, E. Sadowska and Sz. Wąsowicz, A note on separation by subadditive and sublinear functions, Ann.Math.Silesianae 14 (2000), 29-35.
      40. M. Balaj and K. Nikodem, Remarks on Bárány's theorem and affine selections, Discrete Mathematics 224 (2000), 259-263.
      41. K. Nikodem, Zs. Páles and Sz. Wąsowicz, Multifunctions with selections of convex and concave type, Mathematica Pannonica 11/2 (2000), 249-260.
      42. K. Nikodem, Mazur's criterion for continuity of convex set-valued maps, Rocznik Nauk.-Dydakt. AP w Krakowie 204, Prace Mat.17 (2000), 191-195.
      43. K. Nikodem, Continuity properties of midconvex set-valued functions, Aequationes Math.62 (2001), 175-183.
      44. K. Nikodem and Zs. Páles, On approximately Jensen-convex and Wright-convex functions, C.R. Math. Rep. Acad. Sci. Canada 23 (2001), 141-147.
      45. G. Kassay and K. Nikodem, Lagrangian multiplier rule for set-valued optimization, Nonlinear Analysis Forum 6 (2001), 363-369.
      46. R. Ger and K. Nikodem, A characterization of stationary sets for the class of Jensen convex functions, Functional Equations- Results and Advances (Z.Daróczy and Z.Páles - eds.), Kluwer Academic Publishers 2002, 25-28.
      47. M. Adamek, K. Nikodem and Zs. Páles, On (K,lambda) - convex set-valued maps, Radovi Mat. 11 (2002/2003), 183-191.
      48. K. Nikodem, Continuity properties of convex-type set-valued maps, J.of Inequalities in Pure and Appl. Math Vol.4, Issue 3, Art. 52, 2003.
      49. A. Gilányi, K. Nikodem and Zs. Páles, Bernstain-Doetsch type results for quasiconvex functions, Math. Inequal. Appl. 7/2 (2004),169-175.
      50. K. Nikodem and Zs. Páles, On t-convex functions, Real Anal. Exchange 29 (1) (2003/2004), 219-228.
      51. K. Nikodem and W. Zhang, On a multivalued iterative equation, Publ. Math. Debrecen 64 / 3-4 (2004), 427-435.
      52. K. Nikodem, Remarks additive set - valued functions, Analele Univ. Oradea Fasc. Mat. 11 (2004), 175-180.
      53. K. Nikodem, W. Zhang and B. Xu, Convex solutions of polynomial-like iterative equations, J. Math. Anal. Appl. 315 (2006) 29-40.
      54. M. Adamek, A.Gilányi and K. Nikodem, A note on three-parameter families and generalized convex functions, J. Math. Anal. Appl. 330 (2007) 829-835.
      55. K. Nikodem and Zs. Páles, Generalized Convexity and Seperation Theorems, Journal of Convex Analysis, Volume 14 (2007), No. 2, 239-247.
      56. K. Nikodem, T. Riedel and P. Sahoo, The stability problem of the Hermite-Hadamard inequality, Math. Inequal. Appl., 10/2 (2007), 359-363.
      57. K. Nikodem, Leonhard Euler i najpiękniejszy wzór matematyczny, Świat Techniki, Wydawnictwo ATH, 2007, s.75-78.
      58. K. Nikodem and Zs. Páles, Note on t-quasiaffine functions, Annales Univ. Sci. Budapest., Sect. Comp. 29 (2008) 127-139.
      59. K. Nikodem and D. Popa, On single-valuedness of set-valued maps satisfying linear inclusions, Banach J. Math. Anal. 3 (2009), no. 2, 44-51.
      60. M. S. Moslehian, K. Nikodem and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, J. Math. Anal. Appl. 355 (2009) 717-724.
      61. K. Nikodem and D. Popa, On selections of general linear inclusions, Publ. Math. Debrecen, 75/1-2 (2009), 239-249.
      62. K. Nikodem and M. Nikodem, Remarks on t-quasiconvex functions, Math. Inequal. Appl., Vol. 12, No. 4 (2009), 711-717.
      63. K. Nikodem and Zs. Páles, Minkowski sums of Cantor-type sets, Colloquium Math. 119 (2010), 95-108.
      64. N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aeqationes Math. 80 (2010), 193-199.
      65. A. Azocar, J. Gimenez, K. Nikodem and J. L. Sánchez, On strongly midconvex functions, Opuscula Math. 31 (2011), 15-26.
      66. K. Nikodem and Zs. Páles, Characterizations of inner product spaces by strongly convex functions, Banach J. Math. Anal. 5 (2011), 83-87.
      67. R. Ger and K. Nikodem, Strongly convex functions of higher order, Nonlinear Anal. 74 (2011), 661-665.
      68. N. Merentes, K. Nikodem, S. Rivas, Remarks on strongly Wright-convex functions, Ann. Polon. Math. 102.3 (2011), 271-278.
      69. B. Xu, K. Nikodem, W. Zhang, On a multivalued iterative equation of order n, J. Conv. Anal. 18 (2011), 673 - 686.
      70. H. Angulo, J. Gimenez, A. M. Moros, K. Nikodem, On strongly h-convex functions, Ann. Funct. Anal. 2 (2011), 87 - 93.
      71. J. Mako, K. Nikodem, Zs. Páles, On strong (alfa, F)-convexity, Math. Inequal. Appl., Vol. 15 No. 2 (2012), 289-299.
      72. K. Nikodem, T. Rajba, Sz. Wąsowicz, On the classes of higher-order Jensen-convex functions and Wright-convex functions, J. Math. Anal. Appl. 396 (2012), 261-269.
      73. K. Nikodem, T. Rajba, Sz. Wąsowicz, Functions Generating Strongly Schur-Convex Sums, Inequalities and applications 2010: dedicated to the memory of Wolfgang Walter / ed. Catherine Bandle (2012), 175-182.
      74. A. Azocar, K. Nikodem, G. Roa, Fejer-type inequalities for strongly convex functions, Ann. Math. Silesianae 26 (2012), 43-54.
      75. H. Leiva, N. Merentes, K. Nikodem, J.L. Sanchez, Strongly convex set-valued maps, J. Glob. Optim. (2013)
      76. F. C. Mitroi, K. Nikodem, Sz. Wąsowicz, Hermite-Hadamard inequalities for convex set-valued functions, Demonstratio Math. 96 (2013), 655-662.
      77. O. Mejia, N. Merentes, K. Nikodem, Strongly concave set-valued maps, Math. Aeterna 4, (2014), 477-487.
      78. C. Gonzales, K. Nikodem, Zs. Páles, G. Roa, Bernstein-Doetsch type theorems for set-valued maps of strongly and approximately convex and concave types, Publ. Math. Debrecen 84/ 1-2 (2014), 229-252.
      79. K. Nikodem, J.L. Sánchez, L. Sánchez, Jensen and Hermite-Hadamard inequalities for strongly convex set-valued maps, , Math. Aeterna 4, (2014), 979-987.
      80. A. Gilányi, N. Merentes, K. Nikodem, Zs. Páles, Characterizations and decomposition of strongly Wright-convex functions of higher order, Opuscula Math.35 (2015), 37-46
      81. K. Nikodem Strongly convex functions and related classes of functions, In Th. M. Rassias (Ed) Handbook of FunctionalEquations. Functional Inequalities, Springer Optimalizations and its Application. Vol. 95 (2015), 365-405.
      82. D. Kotrys, K. Nikodem, Quasiconvex stochastic processes and a separation theorem, Aequationes Mathematicae.89 (2015), 41-48
      83. A. Gilányi, N. Merentes, K. Nikodem, Zs. Páles, On higher-order convex functions with a modulus, Grazer Math. Ber.363 (2015), 66-74
      84. M. Klaričić Bakula, K. Nikodem On the converse Jensen inequality for strongly convex functions, J. Math. Anal. Appl. 434 (2016), 516-522.
      85. N. Merentes, K. Nikodem Strong convexity and separation theorem, Aequationes Mathematicae 90 (2016), 47-55.
      86. L. Gonzáles, D. Kotrys, K. Nikodem Separation by convex and strongly convex stochastic processes, Publ. Math. Debrecen 89/3 (2016), 365-372.
      87. T. Lara, N. Merentes, K. Nikodem Strong h-convexity and separation theorem, Int. J. Analysis.Art ID 7160348 (2016)
      88. W. Jarczyk, K. Nikodem On some properties of strictly convex functions., Math. Ineq. Appl. 19 (2016), 1413-1416.
      89. A. Gilányi, C. Gonzales, K. Nikodem, Zs. Páles, Bernstein-Doetsch type theorems with Tabor type error terms for set-valued maps, Set-Valued Var. Anal. 25 (2017), 441-462
      90. H.R. Moradi, M.E. Omidvar, M.A. KHAN, K. Nikodem, Around Jensen's inequality for stronglyconvex functions, Aequat.Mat. 92 (2018), 25-37
      91. D. Kotrys, K. Nikodem, Separation by Jensen and affine stochastic processes, Aequat. Mat. 92 (2018), 111-122
      92. M. Klaričić Bakula, K. Nikodem Converse Jensen inequality for strongly convex set-valued maps, Math. Inequal.: 12 (2)(2018), 545-550.
      93. S.S. Dragomir, K. Nikodem, Jensen's and Hermite-Hadamard's type inequalities for lower and strongly convex functions on normed spaces, Bull. Iran. Math. Soc.: 44 (2018), 1337-1349
      94. S.S. Dragomir, K. Nikodem, Functions generating (m, M, &psi) - Schur-convex sums, Aequat. Math: 93 (2019)),79-90
      95. E.Jabłońska, K. Nikodem, K-midconvex and K-midconcave set-valued maps bounded on"large" sets,J. Conv.Anal.26(2) (2019),563-572
      96. E.Jabłońska, K. Nikodem, Continuity properties of K-midconvex and K-midconcave set-valued maps, Math. Ineq. Appl. 22 (2019), 1081-1089.
      97. Nikodem Kazimierz, Set-valued means. Set-Valued Var Anal. (2020), 28, 559 – 568,
      98. Kotrys Dawid, Nikodem Kazimierz, Stochastic processes generating Schur-convex sums, Aequat. Math. (2020), 94, 447-453,
      99. Nikodem Kazimierz, Rajba Teresa, Ohlin and Levin-Ste?kin-type results for strongly convex functions, Anna. Math. Silesianae, (2020), 34, 123-132
      100. Nikodem Kazimierz, Rajba Teresa Ohlin-type theorem for convex set-valued maps, Results Maths, (2020), 75, 1-10,
      101. EL-Fassi Iz-iddine, El-Hady El-Sayed, Nikodem Kazimierz, On set-valued solutions of a generalized bi-quadratic functional equation, Results Math, (2020), 75, 1-20,
      102. Nikodem Joanna, Nikodem Kazimierz. Fuzzy means and HGA-type inequalities, Journal of Mathematical Inequalities, (2021) vol. 15, no. 4, 1487-1497
      103. Jabłońska Eliza, Nikodem Kazimierz. K-subadditive and K-superadditive set-valued functions bounded on "large" sets, Aequationes Mathematicae, (2021) vol. 95, 1221-1231
      104. Klaričić Bakula Milica, Nikodem Kazimierz. Ohlin type theorem and its applications for strongly convex set-valued maps, Journal of Convex Analysis, (2022) vol. 26, 221-229
      105. EL-Fassi Iz-iddine, Nikodem Kazimierz, Popa Dorian. Set-valued solutions of a two-variable functional equation with involutions, Aequationes Mathematicae, (2022) vol. 96, 453-464
      106. Nikodem Kazimierz, Rajba Teresa. On Hermite-Hadamard inequalities for (k,h)-convex set-valued maps, Mathematical Inequalities and Applications, (2022) vol. 25, s. 467-475
  10. Text-book:
    • J. Nikodem, K. Nikodem, Matematyka dla szkół średnich, Wydawnictwo Park, Bielsko-Biała, 1992; ( 9 reissues in the years 1994 - 2009).
    		11.
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