  We investigate on some Appel-type orthogonal polynomial sequences on
q-quadratic lattices and we provide some entire new characterizations of the
Al-Salam Chihara polynomials (including the Rogers q-Hermite polynomials). The
corresponding forms are well described. The proposed method can be applied to
similar and to more general problems involving the Askey-Wilson and the
Averaging operators, in order to obtain new characterization theorems for
classical and semiclassical orthogonal polynomials on lattices.
