Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 3 : pp. 236–243
Abstract
Let $P(z)$ be a polynomial of degree $n$ and for any complex number $\alpha$, let $D_{\alpha}P(z)=nP(z)+(\alpha-z)P'(z)$ denote the polar derivative of the polynomial $P(z)$ with respect to $\alpha$. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n3.2
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 3 : pp. 236–243
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Polar derivative polynomials inequalities maximum modulus growth.