Volume 29, Issue 4
New Inequalities on $L_{\gamma}$-Spaces

Anal. Theory Appl., 29 (2013), pp. 390-400.

Published online: 2013-11

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• Abstract

We consider for a fixed $\mu$, the class of polynomials $$P_{n,\mu,s}:=\Bigg\{ P(z) =z^s(a_nz^{n−s}+ \sum^{n-s}_{j=\mu}a_{n−j}z^{n−j−s}); 1≤\mu≤n−s\Bigg\}$$ of degree $n$, having all zeros in $|z|≤k,$ $k≤1$, with $s$-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

30A10, 30C10, 30D15

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@Article{ATA-29-390, author = {}, title = {New Inequalities on $L_{\gamma}$-Spaces}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {4}, pages = {390--400}, abstract = {

We consider for a fixed $\mu$, the class of polynomials $$P_{n,\mu,s}:=\Bigg\{ P(z) =z^s(a_nz^{n−s}+ \sum^{n-s}_{j=\mu}a_{n−j}z^{n−j−s}); 1≤\mu≤n−s\Bigg\}$$ of degree $n$, having all zeros in $|z|≤k,$ $k≤1$, with $s$-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n4.8}, url = {http://global-sci.org/intro/article_detail/ata/4533.html} }
TY - JOUR T1 - New Inequalities on $L_{\gamma}$-Spaces JO - Analysis in Theory and Applications VL - 4 SP - 390 EP - 400 PY - 2013 DA - 2013/11 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n4.8 UR - https://global-sci.org/intro/article_detail/ata/4533.html KW - Polynomial, Zygmund inequality, polar derivative. AB -

We consider for a fixed $\mu$, the class of polynomials $$P_{n,\mu,s}:=\Bigg\{ P(z) =z^s(a_nz^{n−s}+ \sum^{n-s}_{j=\mu}a_{n−j}z^{n−j−s}); 1≤\mu≤n−s\Bigg\}$$ of degree $n$, having all zeros in $|z|≤k,$ $k≤1$, with $s$-fold zeros at the origin. In this paper, we have obtained inequalities in the reverse direction for the above class of polynomials. Besides, extensions of some Turan-type inequalities for the polar derivative of polynomials have been considered.

Abdullah Mir, Bilal Dar & Sajad Amin Baba. (1970). New Inequalities on $L_{\gamma}$-Spaces. Analysis in Theory and Applications. 29 (4). 390-400. doi:10.4208/ata.2013.v29.n4.8
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