Commutativity of set-valued cosine families

Andrzej Smajdor; Wilhelmina Smajdor

Open Mathematics (2014)

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

Abstract

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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 ∘ F s ( x ) = F s ∘ F t ( x ) f o r s , t ⩾ 0 a n d x ∈ K .

How to cite

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Andrzej 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 -

References

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