Growth of polynomials whose zeros are outside a circle

If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.