On Opial’s Type Integral Inequalities

Abstract

In the article we establish some new Opial’s type inequalities involving higher order partial derivatives. These new inequalities, in special cases, yield Agarwal-Pang’s, Pachpatte’s and Das’s type inequalities.

Opial-Jensen and functional inequalities for convex functions

“…Opial's inequality and its generalizations play an important role in determining the existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations. Recently, a large number of articles have appeared in the literature dealing with different types of evidence and various generalizations of Opial inequalities, see [5]- [9], [10]- [23].…”