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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
Czasopismo
Rocznik
Tom
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