Copyright © 2010 Yilmaz Simsek and Mehmet Acikgoz. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The main object of this paper is to construct a new generating function of the () Bernstein-type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the () Bernstein-type polynomials. We also give relations between the () 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 () Bernstein-type polynomials. Moreover, we give some applications and questions
on approximations of () Bernstein-type polynomials, moments of some distributions in