Turán-Type inequalities for polynomials with restricted Zeros -II

Abstract

If is a polynomial of degree n, having all its zeros in |z| ≤ k, k ≤ 1, then it was shown by Govil [Proc. Amer. Math. Soc., 41 (2) (1973), 543–546] that

In this paper we generalize as well as improve the above inequality and some other related inequalities by extending them to the polar derivative of a polynomial of degree n≥ 3having all its zeros in |z| ≥ k, k ≤ 1 with s-fold zeros at the origin, where 0≤s≤n. AMS Mathematics Subject Classification (2000): 30A10, 30C10, 30C15.

Keywords and phrases:

• Polynomials
• Polar Derivative
• Zeros
• Extremal Problems