- Tytuł:
- Some quadratic integral inequalities of Opial type
- Autorzy:
- Kuchta, Małgorzata
- Powiązania:
- https://bibliotekanauki.pl/articles/1311184.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
absolutely continuous function
integral inequality - Opis:
- We derive and investigate integral inequalities of Opial type: $∫_I s|hḣ|dt ≤ ∫_I rḣ² dt$, where h ∈ H, I = (α,β) is any interval on the real line, H is a class of absolutely continuous functions h satisfying h(α) = 0 or h(β) = 0. Our method is a generalization of the method of [3]-[5]. Given the function r we determine the class of functions s for which quadratic integral inequalities of Opial type hold. Such classes have hitherto been described as the classes of solutions of a certain differential equation. In this paper a wider class of functions s is given which is the set of solutions of a certain differential inequality. This class is determined directly and some new inequalities are found.
- Źródło:
-
Annales Polonici Mathematici; 1996, 63, 2; 103-113
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł