Abstract
In this paper, we generalize some existing discrete Pachpatte type inequalities to more general situations. These inequalities in turn can be applied to study various qualitative as well as quantitative properties of solutions of various finite difference and sum-difference equations and its variants.
Highlights
The role played by finite difference inequalities in the development of the theory of finite difference equations is well known
The desire to widen the scope of applications of finite difference equations has resulted into the necessity of discovering various new finite difference inequalities in order to study the qualitative as well as quantitative behavior of solutions of such equations
In [5, 6, 7], Pachpatte investigated a number of new finite difference inequalities which are useful in the study of new classes of difference and sum-difference eqautions
Summary
The role played by finite difference inequalities in the development of the theory of finite difference equations is well known. (Pachpatte’s Inequality [5]) Let a(t) be nonnegative function defined on N0 and c ≥ 1 be a constant. We state and prove some new nonlinear difference inequalities of Pachpatte type and we obtain a bound on an unknown function, which can be used in the analysis of various problems in the theory of nonlinear difference and sum-difference equations.
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