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Abstrakty
Using the Rådström–Hörmander theorem on embedding of the hyperspace of closed convex sets in a Banach space, we prove multivalued versions of some results known for real functions.
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Rocznik
Tom
Strony
259--271
Opis fizyczny
Bibliogr. 17 poz.
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autor
- Mathematics Department, Silesian University, Bankowa 14 40-007 Katowice, Poland, kucia@ux2.math.us.edu.pl
Bibliografia
- [1] C. M. Aseev, Approximation of semicontinuous multivalued mappings by continuous ones, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 460-476 (in Russian); English transl.: Math. USSR-Izv. 20 (1983), 435-448.
- [2] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977.
- [3] M. M. Čoban and D. M. Ipate, Approximation of multivalued mappings by continuous mappings, Serdica 17 (1991), 127-136 (in Russian).
- [4] F. S. De Blasi, Characterizations of certain classes of semicontinuous multifunctions by continuous approximations, J. Math. Anal. Appl. 106 (1985), 1-18.
- [5] F. S. De Blasi and G. Pianigiani, Remarks on Hausdorff continuous multifunctions and selections, Comment. Math. Univ. Carolin. 24 (1983), 553-561.
- [6] J. Dugundji and A. Granas, Fixed Point Theory, PWN, Warszawa, 1982.
- [7] R. Engelking, General Topology, PWN, Warszawa, 1977.
- [8] K. M. Garg, On the classification of set-valued functions, Real Anal. Exchange 9 (1983-84), 86-93.
- [9] —, A general nonseparable theory of functions and multifunctions, ibid., 317-335.
- [10] A. Gavioli, Approximation from the exterior of a multifunction and its application in the “sweeping process”, J. Differential Equations 92 (1991), 373-383.
- [11] L. Hörmander, Sur la fonction d’appui des ensembles convexes dans un espace localement convexe, Ark. Mat. 3 (1954), 181-186.
- [12] A. Kucia, Remarks on intersections of semicontinuous multifunctions, in preparation.
- [13] E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382.
- [14] H. Rädström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
- [15] D. Repovš and P. V. Semenov, Continuous Selections of Multivalued Mappings, Kluwer, Dordrecht, 1998.
- [16] A. A. Tolstonogov, A theorem on the extension of continuous multivalued maps and its applications, Mat. Zametki 42 (1987), 581-593 (in Russian); English transl.: Math. Notes 42 (1987), 821-827.
- [17] R. Urbański, A generalization of the Minkowski-Radström-Hörmander Theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 709-715.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0008-0025