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Hukuhara's Derivative and Concave Iteration Semigroups of Linear Set-Valued Functions
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A. Smajdor
Published/Copyright:
June 7, 2010
Abstract
Let K be a closed convex cone with the nonempty interior in a real Banach space and cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft : t ≥ 0} is a concave iteration semigroup of continuous linear set-valued functions Ft : K → cc(K) with F0(x) = {x} for x ∈ K, then
DtFt(x) = Ft(G(x))
for x ∈ K and t ≥ 0, where DtFt(x) denotes the Hukuhara derivative of Ft(x) with respect to t and
for x ∈ K.
Received: 2000-08-08
Revised: 2001-10-29
Published Online: 2010-06-07
Published in Print: 2002-December
© Heldermann Verlag
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Articles in the same Issue
- Mathematical Analysis and Optimal Control Problems for the Perturbation of the Primitive Equations of the Ocean with Vertical Viscosity
- On Density Topologies with Respect to Invariant σ-Ideals
- Singularly Perturbed Systems of Volterra Equations
- Nonlocal in Time Problems for Evolution Equations of Second Order
- Oscillation of Solutions to Nonlinear Neutral Delay Differential Equations
- On the Order Structure of Time Projection
- Hukuhara's Derivative and Concave Iteration Semigroups of Linear Set-Valued Functions
