Volume 31, Issue 3
On an Inequality of Paul Turan Concerning Polynomials-II

Anal. Theory Appl., 31 (2015), pp. 236-243.

Published online: 2017-07

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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 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.

30A10, 30C10, 30C15

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@Article{ATA-31-236, author = {}, title = {On an Inequality of Paul Turan Concerning Polynomials-II}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {3}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n3.2}, url = {http://global-sci.org/intro/article_detail/ata/4636.html} }
TY - JOUR T1 - On an Inequality of Paul Turan Concerning Polynomials-II JO - Analysis in Theory and Applications VL - 3 SP - 236 EP - 243 PY - 2017 DA - 2017/07 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n3.2 UR - https://global-sci.org/intro/article_detail/ata/4636.html KW - Polar derivative, polynomials, inequalities, maximum modulus, growth. 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 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.

A. Mir. (1970). On an Inequality of Paul Turan Concerning Polynomials-II. Analysis in Theory and Applications. 31 (3). 236-243. doi:10.4208/ata.2015.v31.n3.2
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