Volume 29, Issue 4
Some Inequalities Concerning the Polar Derivative of a Polynomial-II

Anal. Theory Appl., 29 (2013), pp. 384-389.

Published online: 2013-11

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• Abstract

In this paper, we consider the class of polynomials $P(z)=a_{n}z^{n}+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}$, $1\leq \mu\leq n$, having all zeros in $|z|\leq k$, $k\leq 1$ and thereby present an alternative proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial.

30A10, 30C10, 30C15

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@Article{ATA-29-384, author = {}, title = {Some Inequalities Concerning the Polar Derivative of a Polynomial-II}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {4}, pages = {384--389}, abstract = {

In this paper, we consider the class of polynomials $P(z)=a_{n}z^{n}+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}$, $1\leq \mu\leq n$, having all zeros in $|z|\leq k$, $k\leq 1$ and thereby present an alternative proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n4.7}, url = {http://global-sci.org/intro/article_detail/ata/4532.html} }
TY - JOUR T1 - Some Inequalities Concerning the Polar Derivative of a Polynomial-II JO - Analysis in Theory and Applications VL - 4 SP - 384 EP - 389 PY - 2013 DA - 2013/11 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n4.7 UR - https://global-sci.org/intro/article_detail/ata/4532.html KW - Polar derivative of a polynomial. AB -

In this paper, we consider the class of polynomials $P(z)=a_{n}z^{n}+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}$, $1\leq \mu\leq n$, having all zeros in $|z|\leq k$, $k\leq 1$ and thereby present an alternative proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial.

A. Mir & B. Dar. (1970). Some Inequalities Concerning the Polar Derivative of a Polynomial-II. Analysis in Theory and Applications. 29 (4). 384-389. doi:10.4208/ata.2013.v29.n4.7
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