Some Sharpening and Generalizations of a result of T. J. Rivlin

N. K. Govil, Eze R. Nwaeze

Let $p(z)=a_0+a_{1}z+a_2{z}^2+a_3{z}^3+\cdots +a_n{z}^n$ be a polynomial of degree $n$. Rivlin \cite{Rivlin} proved that if $p(z)\ne 0$ in the unit disk, then for $0<r\le 1$, $\displaysty…