Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 6

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

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

100%
Smajdor A.
Annales Polonici Mathematici
|
2004
|
tom 83
|
nr 1
1-10
EN
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 ${F^{t}: t ≥ 0}$ of continuous linear set-valued functions $F^{t}: K → cc(K)$ 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 $D_{t}Φ(t,x) = Φ(t,G(x)) := ⋃ {Φ(t,y): y ∈ G(x)}$, 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 $G(x) := lim_{s → 0+} (F^{s}(x) - x)/s$ for x ∈ K.
2
Content available remote

On absolutely monotone set-valued functions

100%
Smajdor A.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 2
113-118
EN
We define absolutely monotone multifunctions and prove their analyticity on an interval [0,b).
3
Content available remote

Commutativity of set-valued cosine families

64%
Smajdor A., Smajdor W.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1871-1881
EN
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 $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.
4
Content available remote

Concave iteration semigroups of linear continuous set-valued functions

64%
Smajdor A., Smajdor W.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2272-2282
EN
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 $$G(x) = \mathop {\lim }\limits_{s \to 0} {{\left( {F^0 \left( x \right) - F^s \left( x \right)} \right)} \mathord{\left/ {\vphantom {{\left( {F^0 \left( x \right) - F^s \left( x \right)} \right)} {\left( { - s} \right)}}} \right. \kern-\nulldelimiterspace} {\left( { - s} \right)}}$$ for x ∈ K.
5
Content available remote

A theorem of the Hahn-Banach type and its applications

51%
Gajda Z., Smajdor A., Smajdor W.
Annales Polonici Mathematici
|
1992
|
tom 57
|
nr 3
243-252
EN
Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.
6
Content available remote

p-convex iteration groups

26%
Ger R., Smajdor A.
Fundamenta Mathematicae
|
1976
|
tom 91
|
nr 1
29-38
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.