Year: 2016
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 27–37
Abstract
Let $p(z)$ be a polynomial of degree $n$, which has no zeros in $|z|< 1$, Dewan et al. [K. K. Dewan and Sunil Hans, Generalization of certain well known polynomial inequalities, J. Math. Anal. Appl., 363 (2010), pp. 38-41] established $$\Big|zp'(z)+\frac{n\beta}{2}p(z)\Big| \leq \frac{n}{2}\Big\{\Big(\Big|\frac{\beta}{2}\Big|+\Big|1+\frac{\beta}{2}\Big|\Big)\max_{|z|=1}|p(z)|-\Big(\Big|1+\frac{\beta}{2}\Big|-\Big|\frac{\beta}{2}\Big|\Big)\min_{|z|=1}|p(z)|\Big\},$$ for any $|\beta|\leq 1$ and $|z|=1$. In this paper we improve the above inequality for the polynomial which has no zeros in $|z|< k, $ $ k\geq 1$, except $s$-fold zeros at the origin. Our results generalize certain well known polynomial inequalities.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n1.3
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 27–37
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Polynomial $s$-fold zeros inequality maximum modulus derivative.