Volume 30, Issue 3
Some Results on the Polar Derivative of a Polynomial

Anal. Theory Appl., 30 (2014), pp. 306-317.

Published online: 2014-10

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• 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.

• Keywords

Polynomial, zeros, polar derivative, Bernstein inequality.

30A10, 30C10, 30D15

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@Article{ATA-30-306, author = {}, title = {Some Results on the Polar Derivative of a Polynomial}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {3}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.7}, url = {http://global-sci.org/intro/article_detail/ata/4495.html} }
TY - JOUR T1 - Some Results on the Polar Derivative of a Polynomial JO - Analysis in Theory and Applications VL - 3 SP - 306 EP - 317 PY - 2014 DA - 2014/10 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n3.7 UR - https://global-sci.org/intro/article_detail/ata/4495.html KW - Polynomial, zeros, polar derivative, Bernstein inequality. AB -

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.

A. Mir & B. Dar. (1970). Some Results on the Polar Derivative of a Polynomial. Analysis in Theory and Applications. 30 (3). 306-317. doi:10.4208/ata.2014.v30.n3.7
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