ON SHARPENING OF AN INEQUALITY OF TURÁN.

Let P(z) = ∑nv=0 avzv be a polynomial of degree n: Then as a generalization of a well-known result of Turán [18], it was proved by Govil [5] that if P(z) is a polynomial of degree n having all its zeros in |z| ≤ K, K ≥ 1, then (0.1) max |z|=1 |P'(z)|≥ n/1+Kn max |z|=1 |P(z)|. In this paper, we prove a polar derivative generalization of this inequality, which as a corollary gives a sharpening of this inequality (0.1). [ABSTRACT FROM AUTHOR]