Generic
Number  1509 
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Written
Date 
May 16th, 14 
Modified
Date 
May 16th, 14 
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Summary 
A well known result due to Ankeny and Rivlin \cite{1} states that if $p(z)=\sum^n_
{j=0} a_jz^j$ is a polynomial of degree $n$ satisfying $p(z)\ne 0$ for $ z<1$,
then for $R\ge 1$
\begin{eqnarray*}
\max_{z= R} p(z)\le \dfrac{R^n+1}{2}\max_{z= 1} p(z)\,.
\end{eqnarray*}
It was proposed by Professor R.P. Boas Jr.\ to obtain an inequality analogous to
this inequality for polynomials having no zeros in $z0$. In this paper, we
obtain some results in this direction, by considering polynomials of degree $n\ge 2
$, having all its zeros on the disk $z=k$, $k\le 1$.

