A GENERALIZED PACHPATTE'S DISCRETE INEQUALITY WITH DELAYS AND ITS APPLICATIONS

In this paper,Pachpatte's discrete inequality is generalized to a retarded form, where not only delays are included but the contant term is generalized to a positive function.In the generalized inequality,there are more complex terms and the monotonicity of given functions is not required.Estimation of unknown function in the inequality is given by a technique of monotonization.Finally,the result is applied to discuss boundedness and uniqueness of solution for the initial value problem of a delay difference equation.