On Poincaré type integral inequalities

On Friedrichs – Poincaré - type inequalities ✩

Friedrichsand Poincaré-type inequalities are important and widely used in the area of partial differential equations and numerical analysis. Most of their proofs appearing in references are the argument of reduction to absurdity. In this paper, we give direct proofs of Friedrichs-type inequalities in H 1(Ω) and Poincaré-type inequalities in some subspaces of W1,p(Ω). The dependencies of the ine...

On Opial–type Integral Inequalities and Applications

In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. Our results in special cases yield some of the recent results on Opial’s inequality. As application, we prove the uniqueness of the solution of initial value problem involving higher order partial differential equation. Mathematics subject classification (2010): 26D15.

More on Some Hardy Type Integral Inequalities

In 2012, W. T. Sulaiman presented new kinds of Hardy’s integral inequalities. In this paper, we derive some new extensions of the famous Hardy’s integral inequality. The results present direct generalization of the original Hardy inequality. In addition, the corresponding reverse relation is also obtained.

Some generalized Ostrowski-Grüss type integral inequalities

Some Multi–dimensional Hardy Type Integral Inequalities

In this paper we prove some new results concerning multi-dimensional Hardy type integral inequalities and also some corresponding limit Pólya–Knopp type inequalities.