Integral representations of convex and concave set-valued functions

• Autorzy: Piszczek M.
• Języki publikacji: EN

Abstrakty

EN

We will denote by C+ the family of all convex set-valued functions F denned on [a, b} with nonempty compact values, continuous at a, for which there exist all differences F(t) - F(s) as far as a < s < t < b. The main purpose oh this paper is to show that a function F belongs to the family C+ if and only if it is of the form t F(t)=F(a)+^\G(x)dx a for some decreasing set-valued function G.

Słowa kluczowe

EN

convex; Hukuhara's derivative; monotonicity

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 4
• Strony: 727--742
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Piszczek M.

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Bibliografia

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• [4] M. Hukuhara, Integration des application mesurables dont la valeur est un compact convexe, Funkcial. Ekvac. 10 (1967), 205-223.
• [5] E. Klein, A. C. Thompson, Theory of Correspondences, Wiley Interscience, New York, 1984.
• [6] K. Nikodem, K-convex and K-concave set-valued function, Zeszyty Nauk. Politech. Lodz., Mat. 559, Rozprawy Nauk. 144, 1989.
• [7] H. Rådström, An embeldding theorem for space of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
• [8] A. W. Roberts, D. E. Vaberg, Convex Function, Academic Press, New York-London, 1973.