Tytuł artykułu
Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Let K be a closed convex cone with nonempty interior in a real Banach space. The main objective of this paper is to show that if {Gt : t ≥ 0} is a regular sine family of continuous additive set-valued functions associated with {Ft : t ≥ 0}, then Gt are of the form Gt(x) = ∫ t 0 Fu(x)du for x ∈ K,t ≥ 0.
Wydawca
Czasopismo
Rocznik
Tom
Strony
243--258
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland, ewelina.mainka@polsl.pl
Bibliografia
- [1] J. Aczel, Lectures on Functional Equations and their Applications, Academic Press, New York, 1966.
- [2] J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.
- [3] A. Dinghas, Zum Minkowskischen Integralbegriff abgeschlossener Mengen, Math. Z 66(1956), 173-188.
- [4] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105.
- [5] M. Hukuhara, Integration des application mesurables dont la valeur est un compact convexe, Funkcial. Ekvac. 10 (1967), 205-223.
- [6] J. Kisynski, On operator-valued solutions of d’Alembert’s functional equation, I, Colloq. Math. 23 (1971), 107-114.
- [7] J. Kisynski, On operator-valued solutions of d’Alembert’s functional equation, II, Studia Math. 42 (1972), 43-66.
- [8] E. Mainka-Niemczyk, Some properties of set-valued sine families, Opuscula Math. 32 (2012), 157-168.
- [9] B. Nagy, On cosine operator functions in Banach spaces, Acta Sc. Math. 36 (1974), 281-289.
- [10] K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódź., Mat. 559, Rozprawy Nauk. 114, 1989.
- [11] M. Piszczek, Integral representations of convex and concave set-valued functions, Demonstratio Math. 35 (2002), 727-742.
- [12] M. Piszczek, Second Hukuhara derivative and cosine family of linear set-valued functions, Annales Acad. Paed. Cracoviensis. Studia Math. 5 (2006), 87-98.
- [13] M. Piszczek, On multivalued cosine families, J. Appl. Anal. 13 (2007), 57-76.
- [14] M. Piszczek, On cosine families of Jensen set-valued functions, Aequationes Math. 75(2008), 103-118.
- [15] M. Piszczek, On multivalued iteration semigroups, Aequationes Math. 81 (2011), 97-108.
- [16] H. Rädström, An embedding theorem for space of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
- [17] A. Smajdor, Increasing iteration semigroups of Jensen set-valued functions, Aequationes Math. 56(1998), 131-142.
- [18] A. Smajdor, On regular multivalued cosine families, Ann. Math. Sil. 13 (1999), 271— 280.
- [19] M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966), 1-47.
- [20] C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta. Math. Acad. Sci. H. 32 (1978), 75-96.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LODD-0002-0060