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1
Content available remote

Some quadratic integral inequalities of first order

100%
Florkiewicz B., Kuchta M.
Colloquium Mathematicum
|
1998
|
tom 75
|
nr 1
7-18
2
Content available remote

Some quadratic integral inequalities of Opial type

100%
Kuchta M.
Annales Polonici Mathematici
|
1996
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tom 63
|
nr 2
103-113
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.
3
Content available remote

The 123 theorem of Probability Theory and Copositive Matrices

80%
Kovačec A., Moreira M. M. R., Martins D. P.
Special Matrices
|
2014
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tom 2
|
nr 1
EN
Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality for monotone functions.
4
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On the nonlinear stabilization of the wave equation

80%
Guesmia A.
Annales Polonici Mathematici
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1998
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tom 68
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nr 2
191-198
EN
We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.
5
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Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense

70%
Meftah B., Souahi A.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2019
|
tom 18
67-83
EN
In this paper we establish a new fractional identity involving a function oftwo independent variables, and then we derive some fractionalHermite-Hadamard type integral inequalities for functions whose modulus ofthe mixed derivatives are co-ordinated s-preinvex in the second sense.
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