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Warianty tytułu
Języki publikacji
Abstrakty
Let {Ft : t ≥ 0} be a family of continuous additive set-valued functions defined on a convex cone K in a normed linear space X with nonempty convex compact values in X. It is shown that (under some assumptions) a regular sine family associated with {Ft : t ≥ 0} is continuous {Ft : t ≥ 0} is a continuous cosine family.
Czasopismo
Rocznik
Tom
Strony
159--170
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Silesian University of Technology Institute of Mathematics Kaszubska 23, 44-100 Gliwice, Poland, ewelina.mainka@polsl.pl
Bibliografia
- [1] J. Aczél, Lectures on Functional Equations and their Applications, Academic Press, New York and London, 1966.
- [2] J. Aczél, J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.
- [3] C. Berge, Topological Spaces, Including a Treatment of Multi-valued Functions, Vector Spaces and Convexity, Oliver and Boyd, Edinburgh and London, 1963.
- [4] H.O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72–105.
- [5] J. Kisyński, On operator-valued solutions of d’Alembert’s functional equation, I, Colloq. Math. 23 (1971), 107–114.
- [6] J. Kisyński, On operator-valued solutions of d’Alembert’s functional equation, II, Studia Math. 42 (1972), 43–66.
- [7] B. Nagy, On cosine operator functions in Banach spaces, Acta Sci. Math. 36 (1974), 281–289.
- [8] K. Nikodem, On Jensen’s functional equation for set-valued functions, Rad. Mat. 3 (1987), 23–33.
- [9] K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódz., Mat. 559, Rozprawy Nauk. 144, 1989.
- [10] M. Piszczek, Second Hukuhara derivative and cosine family of linear set-valued functions, Ann. Acad. Pedagog. Crac. Stud. Math. 5 (2006), 87–98.
- [11] M. Piszczek, On multivalued cosine families, J. Appl. Anal. 13 (2007), 57–76.
- [12] M. Piszczek, On cosine families of Jensen set-valued functions, Aequationes Math. 75 (2008), 103–118.
- [13] H. Rådström, An embedding theorem for space of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165–169.
- [14] A. Smajdor, On regular multivalued cosine families, Ann. Math. Sil. 13 (1999), 271–280.
- [15] A. Smajdor, Hukuhara’s derivative and concave iteration semigroups of linear set-valued functions, J. Appl. Anal. 8 (2002), 297–305.
- [16] M. Sova, Cosine operator functions, Dissertationes Math. 49 (1966), 1–47.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0007-0013