Abstract
Hahn difference operator D-q,D-omega which is defined by
D(q,omega)g(t) = {g(qt + omega)-g(t)/t(q - 1) vertical bar omega, if t not equal theta:= omega/1 - q, g'(theta), if t = theta
received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form
D(q,omega)x(t) = A(t)x(t) + f(t), t is an element of I,
and
D(q,omega)(2)x(t) + A(t) D(q,omega)x(t) + R(t)x(t) = f(t), t is an element of I,
where A;R : I -> X, and f : I -> X. Here X is a Banach algebra with a unit element e and I is an interval of R containing theta.