On the continuity of the integrable multifunctions

• Autorzy: Piątek B.
• Języki publikacji: EN

Abstrakty

EN

The generalization of the Polovinkin theorem is studied.

Słowa kluczowe

EN

multifunctions; Riemann integral; Aumann integral; Hausdorff metric

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 1
• Strony: 81--88
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Piątek B.

• Silesian University of Technology, Institute of Mathematics, Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

• [1] J.P. Aubin, H. Frankowska, Set-valued analysis, Birkhauser, Boston, Basel, Berlin, 1990.
• [2] R.J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12.
• [3] C. Castaing, M. Valadier, Convex analysis and mesurable multifunction, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
• [4] G. Debreu, Integration of correspondences, Proc. Fifth Berkeley Sympos. Math. Statist, and Probability 2 (1) (1965/66), 351-372, Univ. California Press, Berkeley, Calif.
• [5] A. Dinghas, Zum Minkowskischen Integralbegriff abgeschlossener Mengen, Math. Z. 66 (1956), 173-188.
• [6] N. Dunford, F.T. Schwartz, Linear operators I, Wiley, New York, 1958.
• [7] E. Hille, R. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publ. 31, Providence, 1957.
• [8] M. Kisielewicz, Differential inclusions and optimal control, Kluwer Academic Pres, Dordrecht, 1990.
• [9J B. Piątek, On convex and *-concave multifunction, Ann. Polon. Math. 86 (2005), 165-170.
• (10) E.S. Polovinkin, Riemannian integral of set-valued functions, Lecture Notes in Comput. Sci. 27 (1975), 405-410.
• [11] H. Radstrom, An embedding theorem for spaces of convex sets, Proc. Ainer. Math. Soc. 3 (1952), 165-169.