Volume 2,  Issue 2, 2001

Article 15

ON SOME FUNDAMENTAL INTEGRAL INEQUALITIES AND THEIR DISCRETE ANALOGUES

B.G. PACHPATTE

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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Other papers in this issue

Power-Monotone Sequences and Fourier Series with Positive Coefficients
J. Nemeth

On Some Fundamental Integral Inequalities and their Discrete Analogues
B.G.  Pachpatte

Subharmonic Functions and their Riesz Measure
Raphaele Supper

A Priori Estimate for a System of Differential Operators
Chikh Bouzar

Improved Inclusion-Exclusion Inequalities for Simplex and Orthant Arrangements
Daniel Q. Naiman and Henry P. Wynn

Monotonic Refinements of a Ky Fan Inequality
Kwok K. Chong

Sub-super Solutions and the Existence of Extremal Solutions in Noncoercive Variational Inequalities
V.K. Le

Refinements of Carleman's Inequality
Bao-Quan Yuan 

Inequalities related to the Chebychev Functional Involving Integrals Over Different Intervals
I. Budimir, P. Cerone, and  J. Pecaric

Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions
H.M. Srivastava, Yi Ling and Gejun Bao

Necessary and Sufficient Condition for Existence and Uniqueness of the Solution of Cauchy Problem for Holomorphic Fuchsian Operators
Mekki Terbeche

Bounds for Entropy and Divergence for Distributions over a Two-Element Set
Flemming Topsoe

A Pick Function Related to an Inequality for the Entropy Function
Christian Berg


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