Concave iteration semigroups of linear continuous set-valued functions

• Autorzy: Andrzej Smajdor , Wilhelmina Smajdor
• 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

Concave iteration semigroup; Derivatives of set-valued functions; Riemann integral of set-valued functions

Kategorie tematyczne

• 47D03: Groups and semigroups of linear operators
• 39B12: Iteration theory, iterative and composite equations
• 26E25: Set-valued functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2272-2282

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Andrzej Smajdor

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084, Kraków, Poland

autor

Wilhelmina Smajdor

• Institute of Mathematics, Technical University of Technology, Kaszubska 23, 44-100, Gliwice, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0095-6