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 for x ∈ K.
@article{bwmeta1.element.doi-10_2478_s11533-012-0095-6,
author = {Andrzej Smajdor and Wilhelmina Smajdor},
title = {Concave iteration semigroups of linear continuous set-valued functions},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {2272-2282},
zbl = {1260.26031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0095-6}
}
Andrzej Smajdor; Wilhelmina Smajdor. Concave iteration semigroups of linear continuous set-valued functions. Open Mathematics, Tome 10 (2012) pp. 2272-2282. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0095-6/
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