ISSN 2234-8417 (Online) ISSN 1598-5857 (Print)

 2014's 32,3-4(May)

 GROWTH OF POLYNOMIALS HAVING ZEROS ON THE DISK By K. K. Dewan ..........1509

Generic Number - 1509
References - 0
Written Date - May 16th, 14
Modified Date - May 16th, 14
Visited Counts - 630

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 $|z|=k$, $k\le 1$.

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http://www.springer.com/journal/12190
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