On some fundamental partial integral inequalities

AbstractThis paper presents several new partial integral inequalities in two independent variables which can be used in the analysis of various problems in the theory of partial differential and integral equations as ready and powerful tools. An elementary technique of reducing the integral inequality to second order partial differential inequality and then integrating it by Riemann's method is used to establish our results

On an Inequality of Ostrowski Type in Three Independent Variables

AbstractIn the present paper a new inequality of Ostrowski type in three independent variables is established. The discrete analogue of the main result is also given

On Opial-type integral inequalities

AbstractThe aim of the paper is to establish some new integral inequalities involving two functions and their first order and higher order derivatives. Our results in the special cases yield the well-known Opial inequality and some of its generalizations

Some new finite difference inequalities

AbstractIn this paper, we establish some new finite difference inequalities related to a certain integral inequality arising in the theory of differential equations. The inequalities obtained here can be used as handy tools in the theory of some new classes of finite difference and sum-difference equations

A note on Sobolev type inequalities in two independent variables

AbstractThe aim of the present note is to establish some new integral inequalities of the Sobolev type involving functions of two independent variables and their first-order partial derivatives. The analysis used in the proofs is quite elementary and based on some simple observations and applications of the fundamental inequalities

On two inequalities of the Serrin type

AbstractWe establish two new multidimensional integral inequalities of the Serrin type involving a function and its first order partial derivatives. The analysis used in the proofs is quite elementary and provides new estimates on this type of inequality