scholarly journals Inequalities similar to Opial's inequality involving higher order derivatives

2005 ◽  
Vol 36 (2) ◽  
pp. 111-117
Author(s):  
B. G. Pachpatte
Keyword(s):  
Higher Order ◽  
Opial’S Inequality ◽  
Opial's Inequality ◽  
New Inequalities

In this paper we establish some new inequalities similar to Opial's inequality involving functions and their higher order derivatives. The analysis used in the proofs is elementary and our results provide a new range of nequalities of this type.

scholarly journals Weighted Opial inequalities

2002 ◽  
Vol 33 (1) ◽  
pp. 83-92
Author(s):  
J. J. Koliha ◽  
J. Pecaric
Keyword(s):  
Difference Equations ◽  
Fractional Derivatives ◽  
Kluwer Acad ◽  
General Inequality ◽  
Opial’S Inequality ◽  
Opial's Inequality

This paper presents a class of very general weighted Opial type inequalities. The notivation comes from the monograph of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Acad., Dordrecht 1995) and the work of Anastassiou and Pecaric (J. Math. Anal. Appl. 239 (1999), 402-418).  Assuming only a very general inequality, we extend the latter paper in several directions.  A new result generalizing the original Opial's inequality is obtained, and applications to fractional derivatives are given.

scholarly journals Extensions of Opial’s inequality

1968 ◽  
Vol 26 (2) ◽  
pp. 215-232 ◽  
Author(s):  
Paul Beesack ◽  
Krishna Das
Keyword(s):  
Opial’S Inequality ◽  
Opial's Inequality

A Discrete Analogue of Opial's Inequality

1967 ◽  
Vol 10 (1) ◽  
pp. 115-118 ◽  
Author(s):  
James S. W. Wong
Keyword(s):  
Discrete Analogue ◽  
Absolutely Continuous ◽  
Opial’S Inequality ◽  
Image Position ◽  
Opial's Inequality

In a number of papers [1] - [7], successively simpler proofs were given for the following inequality of Opial [1], in case p=1.Theorem 1. If x(t) is absolutely continuous with x(0)=0, then for any p ≧ 0,(1)Equality holds only if x(t) = Kt for some constant K.

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