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

A. Mir

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.

  • Keywords

Polar derivative polynomials inequalities maximum modulus growth

  • AMS Subject Headings

30A10 30C10 30C15

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COPYRIGHT: © Global Science Press

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@Article{ATA-31-236, author = {A. Mir}, title = {On an Inequality of Pual 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 Pual Turan Concerning Polynomials-II AU - A. Mir 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 KW - polynomials KW - inequalities KW - maximum modulus KW - 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 Pual 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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