Volume 30, Issue 3
On Some Inequalities Concerning Rate of Growth of Polynomials

Anal. Theory Appl., 30 (2014), pp. 290-295.

Published online: 2014-10

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• Abstract

In this paper we consider a class of polynomials $P(z)= a_{0} + \sum_{v=t}^{n} a_{v}z^{v}$, $t\geq 1,$ not vanishing in $|z|<k,$ $k\geq 1$ and investigate the dependence of ${\max_{|z|=1}}|P(Rz)-P(rz)|$ on ${\max_{|z|=1}}|P(z)|,$ where $1 \leq r < R.$ Our result generalizes and refines some known polynomial inequalities.

• Keywords

Polynomial, zero, inequality.

30A10, 30C10, 30D15

mabdullah mir@yahoo.co.in ( Abdullah Mir)

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@Article{ATA-30-290, author = {Abdullah Mir , Imtiaz Hussain , and Dawood , Q. M.}, title = {On Some Inequalities Concerning Rate of Growth of Polynomials}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {3}, pages = {290--295}, abstract = {

In this paper we consider a class of polynomials $P(z)= a_{0} + \sum_{v=t}^{n} a_{v}z^{v}$, $t\geq 1,$ not vanishing in $|z|<k,$ $k\geq 1$ and investigate the dependence of ${\max_{|z|=1}}|P(Rz)-P(rz)|$ on ${\max_{|z|=1}}|P(z)|,$ where $1 \leq r < R.$ Our result generalizes and refines some known polynomial inequalities.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.5}, url = {http://global-sci.org/intro/article_detail/ata/4493.html} }
TY - JOUR T1 - On Some Inequalities Concerning Rate of Growth of Polynomials AU - Abdullah Mir , AU - Imtiaz Hussain , AU - Dawood , Q. M. JO - Analysis in Theory and Applications VL - 3 SP - 290 EP - 295 PY - 2014 DA - 2014/10 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n3.5 UR - https://global-sci.org/intro/article_detail/ata/4493.html KW - Polynomial, zero, inequality. AB -

In this paper we consider a class of polynomials $P(z)= a_{0} + \sum_{v=t}^{n} a_{v}z^{v}$, $t\geq 1,$ not vanishing in $|z|<k,$ $k\geq 1$ and investigate the dependence of ${\max_{|z|=1}}|P(Rz)-P(rz)|$ on ${\max_{|z|=1}}|P(z)|,$ where $1 \leq r < R.$ Our result generalizes and refines some known polynomial inequalities.

Abdullah Mir, Imtiaz Hussain & Q. M. Dawood. (1970). On Some Inequalities Concerning Rate of Growth of Polynomials. Analysis in Theory and Applications. 30 (3). 290-295. doi:10.4208/ata.2014.v30.n3.5
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