Journal ArticleDOI
Some new Opial-type inequalities
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In this paper, some new Opial-type integrodifferential inequalities in one variable are established, which generalize the existing ones which have a wide range of applications in the study of differential and integral equations.Abstract:
In this paper some new Opial-type integrodifferential inequalities in one variable are established. These generalize the existing ones which have a wide range of applications in the study of differential and integral equations.read more
Citations
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Applications of opial and wirtinger inequalities on zeros of third order differential equations
Samir H. Saker,Saudi Arabia +1 more
TL;DR: In this paper, the authors established new inequalities of Lyapunov type for a third order differential equation, which give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zero derivatives.
Inequalities of Opial and Jensen (Improvements of Opial-type inequalities with applications to fractional calculus)
TL;DR: In this paper, Cauchy type mean value theorems are used for Stolarsky type means, all defined by the observed inequalities, and also, they are used to prove the n-exponential convexity for the functionals.
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On Poincaré type integral inequalities
TL;DR: In this article, some new integral inequalities of the Poincare type, on a region of rectangular dimensions, involving many functions in many variables are obtained, which in turn can be used to serve as generators of other integral inequalities.
References
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Journal ArticleDOI
The Existence-Uniqueness Theorem for an nth Order Linear Ordinary Differential Equation
Journal ArticleDOI
An inequality similar to Opial’s inequality
TL;DR: In this article, a sharper version of Opial's original inequality was obtained for linear differential equations of order n, where y(n-1) = O for i=O, 1, n -1 where n? 1.