  The main object of this paper is to construct a new generating function of
the (q-) Bernstein type polynomials. We establish elementary properties of this
function. By using this generating function, we derive recurrence relation and
derivative of the (q-) Bernstein type polynomials. We also give relations
between the (q-) Bernstein type polynomials, Hermite polynomials, Bernoulli
polynomials of higher-order and the second kind Stirling numbers. By applying
Mellin transformation to this generating function, we define interpolation of
the (q-) Bernstein type polynomials. Moreover, we give some applications and
questions on approximations of (q-) Bernstein type polynomials, moments of some
distributions in Statistics.
