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

Andrzej Smajdor

Andrzej Smajdor

Annales Polonici Mathematici, Tome 83 (2004), p. 1-10 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $F^{t} : t \geq 0$ of continuous linear set-valued functions $F^{t} : K \to c c (K)$ 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 $D_{t} Φ (t, x) = Φ (t, G (x)) : = ⋃ Φ (t, y) : y \in G (x)$ , 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 $G (x) : = l i m_{s \to 0 +} (F^{s} (x) - x) / s$ for x ∈ K.

Publié le : 2004-01-01

Zbl 1056.39036

EUDML-ID : urn:eudml:doc:280771

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     author = {Andrzej Smajdor},
     title = {Hukuhara's differentiable iteration semigroups of linear set-valued functions},
     journal = {Annales Polonici Mathematici},
     volume = {83},
     year = {2004},
     pages = {1-10},
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Andrzej Smajdor. Hukuhara's differentiable iteration semigroups of linear set-valued functions. Annales Polonici Mathematici, Tome 83 (2004) pp. 1-10. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-1/