Year: 2011
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 2 : pp. 150–157
Abstract
If $p(z)$ is a polynomial of degree $n$ having all its zeros on $|z| = k$, $k \leq 1$, then it is proved[5] that $$\max_{|z|=1}|p′(z)| \leq\frac{n}{k^{n−1}+k^n}\max_{|z|=1}|p(z)|.$$In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type $p(z) = c_nz^n +\sum\limits_{j=\mu}^{n}c_{n-j}z^{n-j}$, $1 \leq \mu \leq n$. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.1007/s10496-011-0150-3
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 2 : pp. 150–157
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: polynomial zeros inequality polar derivative.
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