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Some quadratic integral inequalities of first order

100%

Florkiewicz B., Kuchta M.

Colloquium Mathematicum

1998

tom 75

nr 1

7-18

Some quadratic integral inequalities of Opial type

100%

Kuchta M.

Annales Polonici Mathematici

1996

tom 63

nr 2

103-113

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

2 Kuchta M.

1 Florkiewicz B.

1 1998

1 1996

Wyniki wyszukiwania

Some quadratic integral inequalities of first order

Some quadratic integral inequalities of Opial type