ON ZERO FREE REGIONS FOR DERIVATIVES OF A POLYNOMIAL.

Let P_n denote the set of polynomials of the form ... with |a| ≤ 1 and |z_k| ≥ 1 for 1 ≤ k ≤ n - m. For the polynomials of the form p(z) = z∏_k=1^n-1(z - z_k), with |z_k| ≥ 1, where 1 ≤ k ≤ n - 1, Brown [2] stated the problem "Find the best constant C_n such that p'(z) does not vanish in |z| < Cn". He also conjectured in the same paper that C_n = .... This problem was solved by Aziz and Zarger [1]. In this paper, we obtain the results which generalizes the results of Aziz and Zarger. [ABSTRACT FROM AUTHOR]