الفهرس 
Title : Stability of hahn difference equations
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Abstract
In this thesis, we study the theory of abstract linear Hahn difference equations of the form A₀(t)D n q,}x(t) + A1(t)D n⁻¹ q,} x(t) + ... + An(t)x(t) = B(t), where B and Ai are mappings from an interval I into a Banach algebra X, i = 1, ..., n. We define the abstract exponential functions, and the abstract trigonometric (hyperbolic) functions. We prove that they are solutions of first and second order linear Hahn difference equations, respectively. We obtain sufficient conditions for many kinds of stability of abstract first order Hahn difference equations in Banach algebras of the from Dq,}x(t) = A(t)x(t) + f(t), t {u2208} I. We use these results to establish these kinds of stability for abstract second order Hahn difference equations of the form D ² q,}x(t) + A(t)Dq,}x(t) + R(t)x(t) = f(t), t {u2208} I where A, R : I {u2192} X, and f : I {u2192} X is continuous at k