- Tytuł:
- Asymptotic behaviour of solutions of difference equations in Banach spaces
- Autorzy:
- Kisiołek, Anna
- Powiązania:
- https://bibliotekanauki.pl/articles/729477.pdf
- Data publikacji:
- 2008
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Banach space
difference equation
fixed point
measure of noncompactness
asymptotic behaviour of solutions - Opis:
-
In this paper we consider the first order difference equation in a Banach space
$Δx_{n} = ∑_{i=0}^∞ a^{i}_{n} f(x_{n+i})$.
We show that this equation has a solution asymptotically equal to a.
As an application of our result we study the difference equation
$Δx_{n} = ∑_{i=0}^∞ a^i_{n}g(x_{n+i}) + ∑_{i=0}^∞ b^{i}_{n}h(x_{n+i}) + y_{n}$
and give conditions when this equation has solutions.
In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness. - Źródło:
-
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 5-13
1509-9407 - Pojawia się w:
- Discussiones Mathematicae, Differential Inclusions, Control and Optimization
- Dostawca treści:
- Biblioteka Nauki
Artykuł