This paper deals with approximating properties of the newly defined
q-generalization of the genuine Bernstein-Durrmeyer polynomials in the case
q>1, whcih are no longer positive linear operators on C[0,1]. Quantitative
estimates of the convergence, the Voronovskaja type theorem and saturation of
convergence for complex genuine q-Bernstein-Durrmeyer polynomials attached to
analytic functions in compact disks are given. In particular, it is proved that
for functions analytic in \left\{ z\in\mathbb{C}:\left\vert z\right\vert
q, the rate of approximation by the genuine
q-Bernstein-Durrmeyer polynomials (q>1) is of order qβn versus 1/n
for the classical genuine Bernstein-Durrmeyer polynomials. We give explicit
formulas of Voronovskaja type for the genuine q-Bernstein-Durrmeyer for
q>1