Abstract

Let $P(z)$ be a polynomial and $P'(z)$ its derivative. In this paper, we shall obtain certain compact generalizations and sharp refinements of some results of Govil, Malik, Turán and others concerning the maximum modulus of $P(z)$ and $P'(z)$ on the unit circle $|z|=1$, which also yields a number of other interesting results for various choices of parameters.

Keywords: Inequalities; zeros of polynomials; derivative; maximum modulus.

MSC: 30C10, 30C15

Pages:  148$-$154     

Volume  66 ,  Issue  2 ,  2014