On the Sincov functional equation

• Autorzy: Piątek B.
• Języki publikacji: EN

Abstrakty

EN

The Riemarm integral, the Hukuhara differences and derivatives will be applied to obtain solutions of the Sincov functional equation.

Słowa kluczowe

EN

multifunctions; Riemann integral; Sincov functional equation; abstract convex cone

PL

multifunkcje; całki Riemanna; równania funkcyjne; równania Sincova

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 875--881
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Piątek B.

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

Bibliografia

• [1] J. Aczel, Lecture on Functional Equations and Their Applications, Academic Press, New York and London, 1966.
• [2] C. Castaing, M. Valadier, Convex Analysis and Mesurables Multifunctions, Lecture Notes in Math. 580, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
• [3] F. S. de Blasi, On the differentiability of multifunctions, Pacific J. Math. 66 (1976), 67-81.
• [4] A. Dinghas, Zum Minkowskischen Integralbegriff abgeschlossener Mengen, Math. Z. 66 (1956), 173-188.
• [5] M. Hukuhara, Intégration des applications mesurables dont la valeur est un compact convexe, Funkcial. Ekvac. 10 (1967), 205-223.
• [6] H. Rådström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
• [7] D. B. Silin , On variation and Riemann integrability of optimal control in linear systems, Dokl. Akad. Nauk SSSR 257 (1981), 548-550 (in Russian).
• [8] D. B. Silin, Riemann integrability of the optimal control in linear time-optimality problems, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), no. 4, 854-864 (in Russian).
• [9] D. B. Silin , On set-valued differentiation and integration, Set-Valued Analysis 5 (1997), 107-146.
• [10] R. Urbański, A generalization of Minkowski-Rådström-Hörmander theorem, Bull. Akad. Pol. Sci. 24(9) (1976), 709-715.