Finite Difference Inequalities Research Articles

Some generalizations of linear finite difference inequalities of Pachpatte type

In this paper, we establish some linear finite difference inequalities and obtain an explicit bound on the unknown function. These inequalities can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some finite difference equations and its variants.

Some nonlinear finite difference inequalities and its applications

Some nonlinear finite difference inequalities and its applications

On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations

Abstract By some new analysis techniques, we generalize the results presented by Pachpatte in [Integral and Finite Difference Inequalities and Applications, volume 205, Elsevier, 2006] and and by S. D. Kendre in [Some nonlinear integral inequalities for Volterra–Fredholm integral equations, Adv. Inequal. App, 2014:Article 21, 2014.] to nonlinear retarded inequalities, and investigate also some new forms. Some applications are also presented in order to illustrate the usefulness of some of our results.

Estimation of Unknown Functions of Iterative Difference Inequalities and Their Applications

We establish some new nonlinear retarded finite difference inequalities. The results that we propose here can be used as tools in the theory of certain new classes of finite difference equations in various difference situations. We also give applications of the inequalities to show the usefulness of our results.

On Boundedness of Random Solutions of Perturbed Stochastic Discrete Systems

Using finite difference inequalities, we study the boundedness of random solutions of the stochastic perturbation discrete system of the linear stochastic discrete system. The stochastic perturbation discrete system includes an operator. We obtain the conditions under which the random solutions of the stochastic perturbation discrete system are bounded.

Some new generalized Volterra–Fredholm type finite difference inequalities involving four iterated sums

In this paper, based on some new generalized Volterra–Fredholm type finite difference inequalities involving four iterated sums, we derive some new explicit bounds for the unknown functions concerned. These inequalities are of more general forms than some existing results in the literature, and are generalization of the main results of Ma [J. Comput. Appl. Math. 233 (2010) 2170–2180]. As application of the established results, we present a Volterra–Fredholm sum-difference equation, and research the qualitative as well as quantitative properties for it.

Some new finite difference inequalities arising in the theory of difference equations

In this work, some new finite difference inequalities in two independent variables are established, which can be used in the study of qualitative as well as quantitative properties of solutions of certain difference equations. The established results extend some existing results in the literature.

New integral and finite difference inequalities in three variables

AbstractThe objective of the present paper is to derive new estimates on some fundamental integral and finite difference inequalities in three variables which can be used as tools in the study of certain integral and sum-difference equations. Some applications are also given to convey the importance of one of our result.

On nonlinear finite difference inequalities in two independent variables

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

On some fundamental finite difference inequalities

The main object of this paper is to establish some new finite difference inequalities which can be used as tools in the study of various problems in the theory of certain classes of finite difference and sum-difference equations.

Inequalities applicable in the theory of partial finite difference equations

The main objective of this paper is to establish some new finite difference inequalities in two independent variables which can be used as handy tools in the theory of certain classes of partial finite difference equations. The analysis used in the proofs is elementary and the results established provide new estimates for these types of inequalities.

On Some Finite Difference Inequalities in Two Independent Variables

In this article, we establish some new finite difference inequalities in two independent variables which can be used as tools in the study of certain classes of finite difference and sum-difference equations.

Inequalities for certain finite difference and sum-diference equations

The aim of the present paper is to establish some basic finite difference inequalities which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in applications in the theory of certain finite difference and sum-difference equations.

Inequalities Applicable in the Theory of Finite Difference Equations

In the present paper we establish some new nonlinear finite difference inequalities applicable in the theory of certain classes of finite difference equations in various different situations. We also present applications of some of the inequalities to show their importance to the literature.

INEQUALITIES RELATED TO A CERTAIN INEQUALITY USED IN THE THEORY OF DIFFERENTIAL EQUATIONS

In this paper we establish some new integral and finite difference inequalities related to a certain integral inequality used in the theory of differential equations. The inequalities obtained here can be used as handy tools in the theory of some new classes of integralral and sum-difference equations.

Some new finite difference inequalities

In this paper, we establish some new finite difference inequalities related to a certain integral inequality arising in the theory of differential equations. The inequalities obtained here can be used as handy tools in the theory of some new classes of finite difference and sum-difference equations.

Finite-difference inequalities and an extension of Lyapunov's method.

Finite-difference inequalities and an extension of Lyapunov's method.