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Volume 30, Issue 4
Inequalities for the Polar Derivatives of a Polynomial

B. A. Zargar

Anal. Theory Appl., 30 (2014), pp. 425-432.

Published online: 2014-11

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  • Abstract

Let $P(z)$ be a polynomial of degree $n,$ having all its zeros in $|z|\leq 1.$ In this paper, we estimate $kth$ polar derivative of $P(z)$ on $|z|=1$ and thereby obtain compact generalizations of some known results which among other things yields a refinement of a result due to Paul Turán.

  • AMS Subject Headings

30C10, 30D15

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COPYRIGHT: © Global Science Press

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@Article{ATA-30-425, author = {}, title = {Inequalities for the Polar Derivatives of a Polynomial}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {4}, pages = {425--432}, abstract = {

Let $P(z)$ be a polynomial of degree $n,$ having all its zeros in $|z|\leq 1.$ In this paper, we estimate $kth$ polar derivative of $P(z)$ on $|z|=1$ and thereby obtain compact generalizations of some known results which among other things yields a refinement of a result due to Paul Turán.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n4.10}, url = {http://global-sci.org/intro/article_detail/ata/4507.html} }
TY - JOUR T1 - Inequalities for the Polar Derivatives of a Polynomial JO - Analysis in Theory and Applications VL - 4 SP - 425 EP - 432 PY - 2014 DA - 2014/11 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n4.10 UR - https://global-sci.org/intro/article_detail/ata/4507.html KW - Polar derivative of a polynomial, maximum modulus, Bernstein's inequality. AB -

Let $P(z)$ be a polynomial of degree $n,$ having all its zeros in $|z|\leq 1.$ In this paper, we estimate $kth$ polar derivative of $P(z)$ on $|z|=1$ and thereby obtain compact generalizations of some known results which among other things yields a refinement of a result due to Paul Turán.

B. A. Zargar. (1970). Inequalities for the Polar Derivatives of a Polynomial. Analysis in Theory and Applications. 30 (4). 425-432. doi:10.4208/ata.2014.v30.n4.10
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