 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 $|z|0$. 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 $|z|=k$, $k\le 1$.
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GROWTH OF POLYNOMIALS HAVING ZEROS ON THE DISK
