- Tytuł:
- On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval
- Autorzy:
- Olszowy, Leszek
- Powiązania:
- https://bibliotekanauki.pl/articles/1912736.pdf
- Data publikacji:
- 2008
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Quadratic Urysohn integral
measure of noncompactness
Tichonov fixed point theorem - Opis:
- We show that \(\omega_0 (X) = \lim_{T\to\infty} \lim_{\varepsilon\to 0} \omega^T (X, \varepsilon)\) is a measure of noncompactness defined on some subsets of the space \(C(\mathbb{R}^+) = \{x\colon \mathbb{R}^+ \to \mathbb{R},\ x\ \text{continuous}\}\) furnished with the distance defined by the family of seminorms \(|x|_n\). Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness.
- Źródło:
-
Commentationes Mathematicae; 2008, 48, 1; 103-112
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł