SOME NONLINEAR INEQUALITIES INVOLVING IMPROPER INTEGRALS AND THEIR DISCRETE ANALOGUES

Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.

BOUNDS ON SOLUTIONS TO SOME NONLINEAR VOLTERRA INTEGRAL INEQUALITIES WITH WEAKLY SINGULAR KERNELS

Bounds on solutions to a new class of nonlinear integral inequalities with weakly singular kernels are established by the de-singularity approach.

A NEW NONLINEAR DISCRETE INEQUALITY AND ITS APPLICATION

A new discrete inequality with the power nonlinearity is obtained which unifies and generalizes some known results due to B.G.Pachpatte. A certain initial value problem of a sum-difference equation is also given to convey the usefulness of the inequality obtained.

A NEW INTEGRAL INEQUALITY WITH POWER NONLINEARITY AND ITS DISCRETE ANALOGUE

A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.