Some Results on the Polar Derivative of a Polynomial

Some Results on the Polar Derivative of a Polynomial

Year:    2014

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 3 : pp. 306–317

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 $P(z)$ with respect to $\alpha$. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some 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.2014.v30.n3.7

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 3 : pp. 306–317

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Polynomial zeros polar derivative Bernstein inequality.

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