Some quadratic integral inequalities of Opial type

• Autorzy: Małgorzata Kuchta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

absolutely continuous function; integral inequality

Kategorie tematyczne

• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 2
• Strony: 103-113

Daty

wydano

1996

otrzymano

1994-06-16

poprawiono

1995-10-16

poprawiono

1995-12-15

Twórcy

autor

Małgorzata Kuchta

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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