 Generic
Number - 1509 |
| References
- 0 |
| Written
Date -
May 16th, 14 |
| Modified
Date -
May 16th, 14 |
| Downloaded
Counts - 541 |
| Visited
Counts - 967 |
| |
| Original
File |
|
|
|
| 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 $|z|=k$, $k\le 1$.
|
|
GROWTH OF POLYNOMIALS HAVING ZEROS ON THE DISK
