# Commutativity of set-valued cosine families

Andrzej Smajdor; Wilhelmina Smajdor

Open Mathematics (2014)

- Volume: 12, Issue: 12, page 1871-1881
- ISSN: 2391-5455

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topAndrzej Smajdor, and Wilhelmina Smajdor. "Commutativity of set-valued cosine families." Open Mathematics 12.12 (2014): 1871-1881. <http://eudml.org/doc/269624>.

@article{AndrzejSmajdor2014,

abstract = {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. If F t: t ≥ 0 is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.},

author = {Andrzej Smajdor, Wilhelmina Smajdor},

journal = {Open Mathematics},

keywords = {Cosine and sine families of set-valued functions; The second order set-valued differential problem; Commutative cosine families; cosine and sine families of set-valued functions; the second order set-valued differential problem; commutative cosine families},

language = {eng},

number = {12},

pages = {1871-1881},

title = {Commutativity of set-valued cosine families},

url = {http://eudml.org/doc/269624},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Andrzej Smajdor

AU - Wilhelmina Smajdor

TI - Commutativity of set-valued cosine families

JO - Open Mathematics

PY - 2014

VL - 12

IS - 12

SP - 1871

EP - 1881

AB - 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. If F t: t ≥ 0 is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.

LA - eng

KW - Cosine and sine families of set-valued functions; The second order set-valued differential problem; Commutative cosine families; cosine and sine families of set-valued functions; the second order set-valued differential problem; commutative cosine families

UR - http://eudml.org/doc/269624

ER -

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