Opial-type integral inequalities involving several higher order derivatives
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TLDR
In this article, the authors established for the first time Opial-type integral inequalities involving a function and several higher order derivatives, which contain some known results of P. R. Beesack and K. M. Das.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1992-06-01 and is currently open access. It has received 53 citations till now. The article focuses on the topics: Differential equation & Initial value problem.read more
Citations
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On some generalizations of dynamic Opial-type inequalities on time scales
TL;DR: In this paper, some new generalizations of dynamic Opial-type inequalities on time scales were proved by using algebraic inequalities, Holder's inequality, and a simple consequence of Keller's chain rule.
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Sharp Opial-type inequalities involving $r$-derivatives and their applications
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On some new double dynamic inequalities associated with Leibniz integral rule on time scales
A. A. El-Deeb,Saima Rashid +1 more
TL;DR: In this paper, the authors give a new proof and formula of Leibniz integral rule on time scales and also apply their inequalities to discrete and continuous calculus to obtain some new inequalities as special cases.
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Sharp Opial-Type Inequalities Involving Higher Order Derivatives of Two Functions
Ravi P. Agarwal,Peter Y. H. Pang +1 more
TL;DR: In this article, a very general Opial-type inequalities involving higher-order derivatives of two functions are presented, and extended and improved versions of several recent results are derived from these inequalities.
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Sharp opial-type inequalities in two variables
Ravi P. Agarwal,Petr Y. H. Pang +1 more
TL;DR: In this paper, sharp Opial-type inequalities in two independent variables involving higher order partial derivatives are presented, and from the particular cases of their results, they then correct as well as improve several recent inequalities.
References
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The Existence-Uniqueness Theorem for an nth Order Linear Ordinary Differential Equation
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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.
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A Discrete Analogue of Opial's Inequality
TL;DR: For any p ≧ 0, (1) equality holds only if x(t) = Kt for some constant K as mentioned in this paper, where k is the number of nodes in the graph.