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On some approximation problems in Musielak-Orlicz spaces of multifunctions

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Abstrakty
EN
We introduce the Musielak-Orlicz spaces of multifunctions Xmphi and Xc,m,phi. We prove that these spaces are complete. Also, we get some convergence and approximation theorems in these spaces.
Wydawca
Rocznik
Strony
393--406
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
  • [1] J. Appell, H. T. Nguyen, P. P. Zabrejko, Multivalued superposition operators in ideal spaces of vector functions. I, II, Indag. Math., N.S. 2(4) (1991) 385-395, 397-409.
  • [2] Z. Artstein, J. A. Burns, Integration of compact set-valued functions, Pacific J. Math. 58 (1975), 297-307.
  • [3] J.-P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston/Basel/Berlin 1990.
  • [4] S. De Blasi, A. Lasota, Daniell's Method in the Theory of the Aumann-Hukuhara Integral of Set-Valued Functions, Lincei-Rend. Sc. fis. mat. e nat. 45 (1968), 252-256.
  • [5] S. De Blasi, A. Lasota, Characterization of the integral of set-valued functions, Lincei-Rend. Sc. fis. mat. e nat. 46 (1969), 154-157.
  • [6] S. Hu, N. S. Papageorgiou, Handbook of Multivalued Analysis Vol. 1: Theory, Kluwer Academic Publishers, Dordrecht/Boston/London 1997.
  • [7] A. Kasperski, Modular approximation by a filtered family of the Hammerstein operators, Demonstratio Math. 17 (1984), 409-427.
  • [8] A. Kasperski, Modular approximation in X¹ϕ by a filtered family of "linear operators", Comment. Math. XXX (1991), 335-341.
  • [9] A. Kasperski, Modular approximation in X¹ϕ by a filtered family of the Hammarstein operators, Comment. Math. XXXII (1992), 69-74.
  • [10] A. Kasperski, Modular approximation in Xϕ by a filtered family of Xϕ - linear operators, Functiones et Approximatio XX (1992), 183-187.
  • [11] A. Kasperski, Musielak-Orlicz spaces of multifunctions, convergence and approximation, Comment. Math. 34 (1994), 99-107.
  • [12] A. Kasperski, Notes on approximation in Musielak-Orlicz spaces of multifunctions, Comment. Math. 34 (1994), 109-122.
  • [13] A. Kasperski, Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions, Comment. Math. Univ. Carolinae 35 (1994), 81-93.
  • [14] B. Mordukchowich, Approximation Methods in the Problems of Optimization and control, Nauka, Moscow 1988 (in Russian).
  • [15] J. Musielak, Modular approximation by a filtered family of linear operators, "Functional Analysis and Approximation, Proc. Conf. Oberwolfach, August 9-16, 1980", Birkhäuser, Basel, 1981, 99-110.
  • [16] J. Musielak, Orlicz Spaces and Modular Spaces, "Lecture Notes in Mathematics", Vol. 1034, Springer, Berlin, 1983.
  • [17] A. Pliś, Remark on measurable set-valued functions, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. IX, 12, (1961), 857-859.
  • [18] S. Rolewicz, Wen Song, On lower semi-continuity and metric upper-semicontinuity of Nemytskii set-valued operators, Z. Anal. Angew. 13 (4) (1994), 739-748.
  • [19] S. Rolewicz, Wen Song, On automatic boudedness of Nemytskii set-valued operators, Studia Math. 113 (1) (1995), 67-72.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0010-0015
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