On Some Fundamental Integral Inequalities and their Discrete Analogues

Volume 2, Issue 2, 2001

Article 15

ON SOME FUNDAMENTAL INTEGRAL INEQUALITIES AND THEIR DISCRETE ANALOGUES

DEPARTMENT OF MATHEMATICS,
MARATHWADA UNIVERSITY,
AURANGABAD 431 004,
(MAHARASHTRA), INDIA
E-Mail: bgpachpatte@hotmail.com

Received 8 November, 2000; accepted 20 January, 2001.
Communicated by: D. Bainov

ABSTRACT. The aim of the present paper is to establish some new integral inequalities on two independent variables and their discrete analogues which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential and finite difference equations.

Key words:
Integral inequalities, discrete analogues, two independent variables, partial differential and difference equations, nondecreasing, nonincreasing, terminal value, non-self-adjoint hyperbolic partial differential equation.

2000 Mathematics Subject Classification:
26D10, 26D15.

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