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2012 | 10 | 6 | 2272-2282
Tytuł artykułu

Concave iteration semigroups of linear continuous set-valued functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let {F t: t ≥ 0} be a concave iteration semigroup of linear continuous set-valued functions defined on a convex cone K with nonempty interior in a Banach space X with values in cc(K). If we assume that the Hukuhara differences F 0(x) − F t (x) exist for x ∈ K and t > 0, then D t F t (x) = (−1)F t ((−1)G(x)) for x ∈ K and t ≥ 0, where D t F t (x) denotes the derivative of F t (x) with respect to t and $$G(x) = \mathop {\lim }\limits_{s \to 0} {{\left( {F^0 \left( x \right) - F^s \left( x \right)} \right)} \mathord{\left/ {\vphantom {{\left( {F^0 \left( x \right) - F^s \left( x \right)} \right)} {\left( { - s} \right)}}} \right. \kern-\nulldelimiterspace} {\left( { - s} \right)}}$$ for x ∈ K.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
6
Strony
2272-2282
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
  • Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084, Kraków, Poland, asmajdor@ap.krakow.pl
  • Institute of Mathematics, Technical University of Technology, Kaszubska 23, 44-100, Gliwice, Poland, w.smajdor@polsl.pl
Bibliografia
  • [1] Berge C., Topological Spaces, Oliver and Boyd, Edinburgh-London, 1963
  • [2] Dinghas A., Zum Minkowskischen Integralbegriff abgeschlossener Mengen, Math. Z., 1956, 66, 173–188 http://dx.doi.org/10.1007/BF01186606[Crossref]
  • [3] Edgar G.A., Measure, Topology, and Fractal Geometry, Undergrad. Texts Math., Springer, New York, 1990 [Crossref]
  • [4] Hukuhara M., Intégration des applications mesurables dont la valeur est un compact convexe, Funkcial. Ekvac., 1967, 10, 205–223
  • [5] Kwiecinska G., On the intermediate value property of multivalued functions, Real Anal. Exchange, 2000/2001, 26(1), 245–260
  • [6] Nikodem K., On concave and midpoint concave set-valued functions, Glasnik Mat., 1987, 22(42)(1), 69–76
  • [7] Nikodem K., On Jensenś functional equation for set-valued functions, Rad. Mat., 1987, 3(1), 23–33
  • [8] Olko J., Concave iteration semigroups of linear set-valued functions, Ann. Polon. Math., 1999, 71(1), 31–38
  • [9] Piszczek M., Integral representations of convex and concave set-valued functions, Demonstratio Math., 2002, 35(4), 727–742
  • [10] Piszczek M., Second Hukuhara derivative and cosine family of linear set-valued functions, Ann. Acad. Pedagog. Crac. Stud. Math., 2006, 5, 87–98
  • [11] Piszczek M., On multivalued iteration semigroups, Aequationes Math., 2011, 81(1–2), 97–108 http://dx.doi.org/10.1007/s00010-010-0034-1[Crossref]
  • [12] Rådström H., An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc., 1952, 3(1), 165–169 http://dx.doi.org/10.2307/2032477[Crossref]
  • [13] Smajdor A., On regular multivalued cosine families, Ann. Math. Sil., 1999, 13, 271–280
  • [14] Smajdor A., Hukuharaś derivative and concave iteration semigrups of linear set-valued functions, J. Appl. Anal., 2002, 8(2), 297–305 http://dx.doi.org/10.1515/JAA.2002.297[Crossref]
  • [15] Smajdor A., On concave iteration semigroups of linear set-valued functions, Aequationes Math., 2008, 75(1–2), 149–162 http://dx.doi.org/10.1007/s00010-007-2876-8[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0095-6
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