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Integral equation arising in the theory of partial differential equations

Pachpatte B. G.

Fasciculi Mathematici

2010

Nr 43

115-126

The aim of the present paper is to study some basic qualitative properties of solutions of a certain integral equation arising in the theory of partial differential equations. The well known Banach fixed point theorem and the new integral inequality with explicit estimate obtained in the present paper are used to establish the results.

New Ostrowski and Gruss type inequalities for double integrals

Pachpatte B.

Demonstratio Mathematica

2006

Vol. 39, nr 4

783-791

In the present paper we establish new Ostrowski and Grüss type inequ- alities for double integrals involving three functions and their partial derivatives. The discrete Ostrowski and Grüss type inequalities for double sums are also given.