Commutativity of set-valued cosine families

• Autorzy: Andrzej Smajdor , Wilhelmina Smajdor
• Języki publikacji: EN

Abstrakty

EN

Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {F t: t ≥ 0} is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.

Słowa kluczowe

EN

Cosine and sine families of set-valued functions; The second order set-valued differential problem; Commutative cosine families

Kategorie tematyczne

• 47D09: Operator sine and cosine functions and higher-order Cauchy problems
• 47H04: Set-valued operators
• 39B52: Equations for functions with more general domains and/or ranges

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 12
• Strony: 1871-1881

Daty

wydano

2014-12-01

online

2014-07-20

Twórcy

autor

Andrzej Smajdor

• Pedagogical University of Cracow

autor

Wilhelmina Smajdor

• Silesian University of Technology

Bibliografia

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• [14] Smajdor A., On regular multivalued cosine families, Ann. Math. Sil. 13 (1999), 271–280
• [15] Smajdor A., Hukuhara’s derivative and concave iteration semigrups of linear set-valued functions, J. Appl. Anal. 8 (2002), 297–305 http://dx.doi.org/10.1515/JAA.2002.297
• [16] Smajdor A., Hukuhara’s differentiable iteration semigrups of linear set-valued functions, Ann. Polon. Math. 83(1) (2004), 1–10 http://dx.doi.org/10.4064/ap83-1-1
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Identyfikatory

DOI

10.2478/s11533-014-0433-y