Hukuhara's differentiable iteration semigroups of linear set-valued functions

• Autorzy: Andrzej 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. A family ${F^{t}: t ≥ 0}$ of continuous linear set-valued functions $F^{t}: K → cc(K)$ is a differentiable iteration semigroup with F⁰(x) = x for x ∈ K if and only if the set-valued function $Φ(t,x) = F^{t}(x)$ is a solution of the problem
$D_{t}Φ(t,x) = Φ(t,G(x)) := ⋃ {Φ(t,y): y ∈ G(x)}$, Φ(0,x) = x,
for x ∈ K and t ≥ 0, where $D_{t}Φ(t,x)$ denotes the Hukuhara derivative of Φ(t,x) with respect to t and $G(x) := lim_{s → 0+} (F^{s}(x) - x)/s$ for x ∈ K.

Kategorie tematyczne

• 39B12: Iteration theory, iterative and composite equations
• 26E25: Set-valued functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 83
• Numer: 1
• Strony: 1-10

Daty

wydano

2004

Twórcy

autor

Andrzej Smajdor

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

Identyfikatory

DOI

10.4064/ap83-1-1