Existence and uniqueness of solutions of Hahn difference equations

Hahn introduced the difference operator D(q,omega)f(t) = (f(qt + omega) - f(t))/(t(q - 1) + omega) in 1949, where 0 < q < 1 and omega > 0 are fixed real numbers. This operator extends the classical difference operator Delta(omega)f(t) = (f(t + omega) - f (t))/omega as the Jackson q-difference operator D(q)f(t) = (f(qt) - f(t))/(t(q - 1)). In this paper, we present new results of the calculus based on the Hahn difference operator. Also, we establish an existence and uniqueness result of solutions of Hahn difference equations by using the method of successive approximations.