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

2005 ◽  
Vol 36 (2) ◽  
pp. 111-117
Author(s):  
B. G. Pachpatte

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.

2002 ◽  
Vol 33 (1) ◽  
pp. 83-92
Author(s):  
J. J. Koliha ◽  
J. Pecaric

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.


1968 ◽  
Vol 26 (2) ◽  
pp. 215-232 ◽  
Author(s):  
Paul Beesack ◽  
Krishna Das

1967 ◽  
Vol 10 (1) ◽  
pp. 115-118 ◽  
Author(s):  
James S. W. Wong

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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