سلوك حلول بعض انواع المعادلات الفرقية

                Behavior of Solutions of Some Types of Difference Equations

                                "Difference equations are relationships between quantities that changes over discrete intervals of time, space...etc. This is frequently appears in the study of biological models, some physical models, business, economics and many other applications, see [9], [15], [21], [25].

                In this thesis, we introduce some basic concepts about the difference calculus, the sum calculus and many other topics that are related to difference equations. Also we introduce some examples about applications of difference equations in different fields. We also study in details some types of difference equations [2], [7], [8], that have the interest of many mathematicians recently [27]. Also we investigate the properties of the solutions of some difference equations studied over Banach spaces [7], [24]. 

   This thesis consists of four chapters.

Chapter One

                In this chapter we introduce the basic concepts and operators in difference calculus. Operators like Δ and Σ are the basic tools used in many applications of difference calculus. Also we investigate the different ways by which the difference and differential calculus are related. Also we show the very high analogy in dealing with the operator Δ and the differentiation

operator also between Σ and the integration operator."