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Open Mathematics

2012 | 10 | 6 | 2272-2282
Tytuł artykułu

Concave iteration semigroups of linear continuous set-valued functions

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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.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
2272-2282
Opis fizyczny
Daty
wydano
2012-12-01
online
2012-10-12
Twórcy
autor
• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084, Kraków, Poland
autor
• Institute of Mathematics, Technical University of Technology, Kaszubska 23, 44-100, Gliwice, Poland
Bibliografia
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• [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]
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