Weighted Hardy and Opial-type inequalities

(1971). Integral Inequalities Involving a Function and its Derivative. The American Mathematical Monthly: Vol. 78, No. 7, pp. 705-741.

Integral Inequalities Involving a Function and its Derivative

On Opial-type integral inequalities

rb 1 b (1) fJ |yy(n) I dx (b ? a)n1 I y(n) 12dx. 2 (He employs (1) to prove uniqueness of the initial value problem for linear differential equations of order n.) Also there are generalizations of Opial's original inequality in other directions. (See, for instance, Calvert [2] and Yang [6].) The purpose of this note is to obtain a sharper version of (1) and other generalizations. THEOREM 1. Let yE C(n-1) [a, b ] be such that y() (a) = O for i=O, 1, n -1 where n ? 1. Let y(n-1) be absolutely continuous and y (n) 1 2 dx < oo . Then,

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An inequality similar to Opial’s inequality

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.

Some new Opial-type inequalities

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Gou-sheng Yang

Papers

On a certain result of Z. Opial