Inequalities for the polar derivative of a polynomial

Let P(z) be a polynomial of degree n which does not vanish in the disk \ z \ < k, where k greater than or equal to 1, then it is known that [GRAPHICS] In this paper, we shall extend the above two inequalities to the polar derivative of P(z) with respect to the point a and obtain several interesting results as special cases. We also extend a famous result of S. Bernstein concerning the maximum modulus of the derivative to the kth polar derivative with respect to points alpha 1, alpha 2, ..., alpha(k); k less than or equal to 1.