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Abstrakty
Let K be a convex cone in a real Banach space. The main purpose of this paper is to show that for a regular cosine family {F t : t ∈ R} of linear continuous multifuoctions Ft: K → cc(X) there exists a linear continuous multifunction H: K → cc(K) such that [wzór].
Wydawca
Czasopismo
Rocznik
Tom
Strony
57--76
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Pedagogical University. Institute of Mathematics, Podchorążych 2, 30-084 Cracow, Poland, magdap@ap.krakow.pl
Bibliografia
- [1] Castaing, Ch., Valadier, M., Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, New York, 1977.
- [2] Hukuhara, M., Integmtion des application mesumbles dont la valeur es t un compact convexe, Funkcial. Ekvac. 10 (1967), 205-223.
- [3] Kisyński, J., On cosine operator functions and one-parameter groups of opemtors,Studia Math. 44 (1972), 93-105.
- [4] Kurepa, S., A cosine function equation in Banach algebras, Acta Sci. Math. (Szeged) 23 (1962), 255-267.
- [5] Łojasiewicz, S., An Introduction to the Theory of Real Punctions, A Willey-Interscience Publication, John Willey & Sons, Ltd., Chichester, 1988.
- [6] Nikodem, K., K-convex and K-concave set-valued function, Zeszyty Nauk. Politech. Lódz. Mat. 559, Rozprawy Nauk. 144, Łódź, 1989.
- [7] Nikodem, K., On concave and midpoint concave set-valued function, Glas. Mat. Ser. III 22 (1987), 69-76.
- [8] Olko, J., Concave interetion semigroups of linear set-valued functions, Ann. Polon. Math. 71 (1999), 31-38.
- [9] Plewnia, J., On a family of a set-valued functions, Publ. Math. Debrecen 46 (1995), 149-159.
- [10] Piszczek, M., Integral representations of convex and concave set-valued functions, Demonstratio Math. 35 (2002), 727-742.
- [11] Piszczek, M., Second Hukuhara derivative and cosine family of linear set-valued functions, Ann. Acad. Paedagogicae Cracoviensis, Studia Math. 5 (2006), 87-98.
- [12] Radstrom, H., An embeldding theorem for space of convex sets, Proc. Amer. Math. Soc. 3 (1952),165-169.
- [13] Smajdor, A., On regular multivalued cosine families, Ann. Math. Sil. 13 (1999),271-280.
- [14] Smajdor, W., Superadditive set-valued functions and Banach-Steinhaus theorem, Rad. Mat. 3 (1987), 203-214.
- [15] Sova, M., Cosine operator functions, Rozprawy Mat. 49 (1966), 1-47.
- [16] Travis, C. C., Webb, G. F., Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungar. 32 (1978), 75-95.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-LOD4-0005-0052