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Ryszard Urbanski - Publications

Mathematical Papers

  1. A theorem concerning set correspondences into uniformly convex Banach spaces, "Funct. Approximatio Comment. Math.", 2, 1976, 263-267.
  2. On set-valued measures and set correspondences, "Funct. Approximatio Comment. Math.", 3, 1976, 259-269.
  3. A generalization of the Minkowski-Rådström-Hörmander theorem, "Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 24, 1976, 709-715.
  4. Weak compactness of the range of a set-valued measure, "Comment. Math.", 19, 1977, 401-402.
  5. Decomposition of set functions with values in a topological semigroups, "Studia Math.", 61, 1977, 115-125.
  6. Lattice properties of the space of convex, closed and bounded subsets of a topological vector space, "Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 27, 1979, 157-162, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  7. Interpolation of compact sublinear operators in generalized Orlicz space of nonsymmetric type, "Topology (Proc. Fourth Colloq., Budapest, 1978), Vol. I Colloq. Math. Soc. Janos Bolyai, North-Holland, Amsterdam",23, 1980, 625-638, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  8. A generalization of the Brooks-Jewett Theorem, "Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 28, 1980, 55-59, (wspólna z W. Orliczem).
  9. Some extension of the Riesz-Thorin theorem to generalized Orlicz spaces $$ L_{M}^{\mu}(T) $$, "Comment. Math.", 22, 1980, 43-61, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  10. Interpolation of sublinear bounded operator in sequence spaces $$ h_{M}^{\mu}(X) $$ of nonsymmetric type, "Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 28, 1980, 45-54, (wspólna z H. Hudzikiem oraz W. Orliczem).
  11. On $$ \sigma $$-additivity of set functions, "Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 28, 1980, 447-452, (wspólna z W. Orliczem).
  12. Riesz-Thorin theorem in generalized Orlicz spaces of nonsymmetric type, "Univ. Beograd. Publ. Elektrotehn. Fac. Ser. Math. Fiz.", 706, 1980, 145-158, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  13. Linear operators in modular spaces. An application to approximation theory, "Aproximation and function spaces (Gdańsk, 1979), North-Holland, Amsterdam-New York", 1981, 279-286, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  14. Linear operators in modular spaces, "Comment. Math.", 23, 1983, 33-40, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  15. Total variation of set-valued measure, "Comment. Math.", 23, 1983, 85-89, (wspólna z W. Orliczem).
  16. A modular space over a field with valuation, "Proc. Int. Conf. on Constructive Function Theory, Varna 1981, Sofia", 1983, 584-589.
  17. Modular space over a field with valuation generated by $$ (\omega,\nu) $$-convex modular, "The Volume dedicated to Professor Jan Mikusiński on the ocassion of his 70th birthday, Studia Math.", 77, 1983, 121-131.
  18. A totally non-atomic set valued measure, "Comment. Math.", 24, 1984, 65-67, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  19. Some analogon of Minkowski functional and its applications to the modular spaces, "Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 32, 1984, 297-302.
  20. A generalization of the Koshi-Shimogaki quasi-norm and a topology in the modular space in the sense of Nakano, "Arch. Math." 45, 1985, 336-373.
  21. On linear functionals in modular spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.", 17, 1985, 287-295, (wspólna z D. Pallaschke).
  22. On modular space over a field with valuation, "Math. Z.", 192, 1986, 405-408.
  23. A note on the law cancellation for p-convex sets, "Arch. Math.", 46, 1986, 445-446.
  24. On locally-Lipschitz quasi-differentiable functions in Banach spaces, "Optimization", 17, 1986, 745-749, (wspólna z D. Pallaschke oraz P. Rechtem).
  25. On modular spaces and p-critical modulars, "Bull. Polish. Acad. Sci. Math.", 35, 1987, 745-749.
  26. On extensions of the second-order derivative, "Bull. Polish. Acad. Sci. Math.", 35, 1987, 751-763, (wspólna z D. Pallaschke oraz P. Rechtem).
  27. On modular and Orlicz space over a field with valuation, "Conf. on Constructive Function Theory, Varna 1987, Sofia", 1988, 466-470.
  28. On quasi-differential function and application to
    optimization theory    , "Wiadomości Mat." 29, 1990, 85-92, (w języku polskim), (wspólna z D. Pallaschke).
  29. On minimal pairs of convex compact sets, "Bull. Polish. Acad. Sci. Math." 39, 1991, 105-109, (wspólna z D. Pallaschke oraz S. Scholtesem).
  30. The space of convex bodies and quasi-differentiable functions, "Proc. Int. Conf. Function Spaces, Poznań 1989, Teubner-Texte zur Mathematik", 120, 1991, 128-132, (wspólna z D. Pallaschke oraz S. Scholtesem).
  31. Generalized Derivatives for Non-Smooth Functions, "Comment. Math.", 31, 1991, 97-114, (wspólna z D. Pallaschke oraz P. Rechtem).
  32. Some Criteria for the minimality of Pairs of Compact
    Convex Sets    , "Zeitschrift für Operation Research ZOR", 37, 1993, 129-150, (wspólna z D. Pallaschke).
  33. Reduction of Quasidifferentials and Minimal Representations, "Mathem. Programming (Series A)", 66, 1994, 161-180, (wspólna z D. Pallaschke).
  34. Quasidifferentiable Functions and Minimal Pairs of Compact Convex Sets, "Dissertationes Math.", 340, 1995, 207-221, (wspólna z D. Pallaschke).
  35. A Continuum of Minimal Pairs of Compact Convex Sets which are not Connected by Translation, "Special Issue in celebration of Professor R. T. Rockafellar's 60th birthday, Journal of Convex Analysis", 3 (1), 1996, 83-95, (wspólna z D. Pallaschke).
  36. On minimal convex pairs of convex compact sets, "Arch. Math.", 67, 1996, 226-238.
  37. C-Minimal Pairs of Compact Convex Sets, "Journal of Convex Analysis", 4 (1), 1997, 1-25, (wspólna z D. Pallaschke oraz W. Urbańską).
  38. Quasidifferentiable Functions and Pairs of Convex Compact Sets, "The Volume dedicated to Professor Hoang Tuy on the ocassion of his 70th birthday, Acta Mathematica Vietnamica", 22 (1), 1997, 223-245, (wspólna z D. Pallaschke).
  39. Pairs of Sets with Convex Union, "Collectanea Mathematica", 48 (4-6), 1997, 791-798.
  40. On Cutting Frustum, "The Volume dedicated to Professor Roman Taberski on the ocassion of his 70th birthday, Funct. Approximatio Comment. Math.", 25, (1997), 165-172.
  41. On a Family of Pairwise Convex Sets, "Comment. Math.", 37, 1997, 275-284.
  42. Minimal Pairs of Bounded Closed Convex Sets, "Studia Math.", 126 (1), 1997, 95-99, (wspólna z J. Grzybowskim).
  43. Decompositions of Compact Convex Sets, "Journal of Convex Analysis", 4 (2), 1997, 333-342, (wspólna z D. Pallaschke).
  44. On Convex Class of Pairs of Convex Bodies, "Proc. Amer. Math. Soc.", 125 (11), 1997, 3397-3403, (wspólna z J. Grzybowskim).
  45. On Minimal Fractions, Comment. Math.", 38, 1998, 149-161.
  46. Critical Points and Point Derivations for Lipschitz functions, "The Volume dedicated to Professor Julian Musielak on the ocassion of his 70th birthday, Funct. Approximatio Comment. Math.", 26, 1998, 165-172, (wspólna z D. Pallaschke).
  47. On Common Summands and Anti-summands of Compact Convex Sets, "Bull. Polish. Acad. Sci. Math.", 47 (1), 1999, 367-377, (wspólna z J. Grzybowskim oraz W. Wiernowolskim).
  48. Invariants of Pairs of compact convex sets, "The Volume dedicated to Professor R. T. Rockafellar's on the ocasion of his 65th birthday, Journal of Convex Analysis", 6 (2), (1999), 367-377, (wspólna z D. Pallaschke).
  49. On pairs of closed bounded convex sets which lay in complementary subspaces, "Function Spaces the Fifth Conference, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, Series", 213, 2000, 165-171, (wspólna z J. Grzybowskim).
  50. Minimal pairs of compact convex sets with applications to quasidifferential calculus, "Chapter III of the Book V. F. Demyanov and A. M. Rubinov Quasidifferentiability and Related Topics, Dedicated to Professor Franco Giannesi on his 65th birthday and to Professor Diethard Pallaschke on his 60th birthday, Nonconvex Optim. Appl. Kluwer Academic Publisher, Dortrecht-Boston-London", 43, 2000, 173-213, (wspólna z D. Pallaschke).
  51. Minimal pairs representing selections of four linear functions in $$ \mathbb R^3 $$, "Journal of Convex Analysis", 7 (2), 2000, 445-452, (wspólna z D. Pallaschke oraz J. Grzybowskim).
  52. General Methods of Constructing Equivalent Minimal Pairs not Unique up to Translation, "Revista Mathemática Complutence", 13 (2), 2000, 383-398, (wspólna z J. Grzybowskim oraz S. Kaczmarkiem).
  53. On separation and order law of cancellation for bounded sets, "Optimization", 51 (3), (2002), 487-496, (wspólna z D. Pallaschke).
  54. On summands of closed bounded convex sets, "Zeitschrift für Analysis und ihre Anwendungen", 21 (4), 2002, 845-850, (wspólna z J. Grzybowskim oraz H. Przybycieniem).
  55. On the number of minimal pairs of compact convex sets that are not translates of one another, "Studia Math.", 158 (1), 2003, 59-63, (wspólna z J. Grzybowskim).
  56. On reduced pairs of bounded closed convex sets,
    "Revista Mathemática Complutence", 16 (2), 2003, 59-63, (wspólna z J. Grzybowskim).
  57. Affine straight lines in family of bounded closed convex sets , "Rendiconti del Circolo Mathematico di Palermo", 53 (2), 2004, 225-230, (wspólna z J. Grzybowskim).
  58. Minimal Pairs of Compact Convex Sets, "Orlicz centenary volume. Proceedings of the conferences The Władysław Orlicz centenary conference and Function spaces VII, Poznań, Poland, July 21-25, 2003. Volume I, Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Center Publications (red. Z. Ciesielski et al.)", 64, 2004, 159-172, (wspólna z D. Pallaschke).
  59. A geometric representation of the Morse fan, "Journal of Global Optimization", 30, 2004, 319-333, (wspólna z D. Pallaschke oraz J. Grzybowskim).
  60. On the Representation Property of Kernels Quasidifferentials, "Journal of Convex Analysis", 11 (2), 2004, 387-390, (wspólna z J. Grzybowskim).
  61. Minimal fractions of compact convex sets, Part of the Book F. Giannessi and A. Maugeri Variational Analysis and Applications, Springer 79, 2005, 791–811, (wspólnie z D. Pallaschke).
  62. Data pre-classification and the separation law for closed bounded sets, "Special Issue dedicated to Professor Franco Giannessi on the occasion of his 70th birthday, Optimization Methods and Software", 20, (2-3), 2005, 213-223, (wspólna z D. Pallaschke oraz J. Grzybowskim).
  63. On inclusion and summands of bounded closed convex sets, "Acta Math. Hungar.", 106 (4). 2005, 293-300, (wspólna z J. Grzybowskim).
  64. Three criteria minimality for pairs of compact convex sets, "The Volume dedicated to Professor Diethard Pallaschke on the ocassion of his 65th birthday, Optimization ", 55 (5-6), (2006), 569-576, (wspólna z J. Grzybowskim).
  65. On Summands Properties and Minkowski Subtraction,
    "Zeitschrift für Analysis und ihre Anwendungen", 26 (2), 2007, 247-260, (wspólna z D. Borowską oraz H. Przybycieniem).
  66. Generalized directional derivatives for locally Lipschitz functions witch satisfy Leibniz rule,
    "Dedicated to the 75th birthday of Professor Stefan Rolewicz, Control and Cybernetics", 36 (4), 2007, 911-924, (wspólna z D. Pallaschke oraz J. Grzybowskim).
  67. Decomposition of the polyhedron from Albrecht Dürer's Melencolia I to a minimal pair of compact convex sets, "The Volume dedicated to Professor Hubert Jongen on the ocassion of his 60th birthday, Optimization", 57 (2), 2008, 337-344, (wspólna z D. Pallaschke oraz J. Grzybowskim).
  68. On Partially Ordered Semigroups and an Abstract Set-Difference, "The Volume dedicated to Professor Boris S. Mordukhovich on the ocassion his 60th birthday, Set-Valued Analysis", 16, 2008, 257-265, (wspólna z D. Pallaschke oraz H. Przybycieniem).
  69. Extreme points of lattice intervals in the Minkowski-Radstrom-Hormander lattice, (with: J. Grzybowski) "Proc. Amer. Math. Soc." 136 (11) (2008), 3957--3962.
  70. On reduction of pairs of bounded closed convex sets, (with: J. Grzybowski, D. Pallaschke) "Studia Math." 189 (1) (2008), 1--12.
  71. Minimal pairs of bounded closed sets as minimal representations of elements of the Minkowski-Radstrom-Hormander spaces (with: J. Grzybowski, D. Pallaschke), Polish Academy of Sciences, Institute of Mathematics, Banach Center Publications {\bf 84} (1) (2009), 31--55.
  72. Crystal growth in terms of Minkowski-Radstrom-Hormander space (with: J. Grzybowski) "Bull. Soc. Sci. Lettr. Łódź" 59 (1) (2009), 91--101.
  73. Reduction of finite exhausters (with: J. Grzybowski, D. Pallaschke) "J. Glob. Optim." 46 (2010), 589--601.
  74. Morse indexes for picewise linear functions (with: D. Pallaschke) "Contemporary Math." 514 (2010), 213--223.
  75. On the amount of minimal pairs of convex sets (with: J. Grzybowski, D. Pallaschke) "Optim. Meth. Soft." 25 (1) (2010), 89--96.
  76. A note on the dual of the Minkowski-Radstrom-Hormander lattices (with: J. Grzybowski, D. Pallaschke) "Pacific J. Optim." 6 (2) (2010), 255--262.
  77. Commutative semigroups with cancellation law: a representation theorem (with: J. Grzybowski, D. Pallaschke, H. Przybycień) "Semigroup Forum" (2011) (published online), DOI 10.1007/s00233-011-9327-5.

Monograph

  1. Pairs of Compact Convex Sets–Fractional Arithmetic with Convex Sets, Math. Appl. 548, Kluwer Academic Publisher, Dortrecht–Boston–London, 2002, (wspólna z D. Pallaschke).

Other papers

  1. "Function Spaces" Proceedings of the Second International Conference, Poznań 1989, Teubner–Texte zur Mathematik 120, 1991, (wspólna z H. Hudzikiem oraz J. Musielakiem).
  2. Przestrzenie modularne, Viro docto atque iusto Juliano Musielak, Poznań 1999, 85–98, (wspólna z R. Płuciennikiem oraz M. Wisłą).
  3. Bruchrechnung mit konvexen Mengen, Karlsruher Transfer 25, 2001, 12–14, (wspólna z D. Pallaschke).
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