Volume 28, Issue 2
$L^p$ Inequalities and Admissible Operator for Polynomials

Anal. Theory Appl., 28 (2012), pp. 156-171.

Published online: 2012-06

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• Abstract

Let $p(z)$ be a polynomial of degree at most $n$. In this paper we obtain some new results about the dependence of$$\Bigg\|p(Rz)−\beta p(rz)+\alpha\Big\{\frac{R+1}{r+1}\Big)^n-|\beta|\Big\} p(rz)\Bigg\|_s$$ on $\|p(z)\|_s$ for every $\alpha$, $\beta \in C$ with $|\alpha| \leq 1$, $|\beta| \leq 1$, $R > r \ge 1$, and $s > 0$. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.

• Keywords

$L^p$ inequality polynomials, Rouche’s theorem, admissible operator.

39B82, 39B52, 46H25

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@Article{ATA-28-156, author = {}, title = {$L^p$ Inequalities and Admissible Operator for Polynomials}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {2}, pages = {156--171}, abstract = {

Let $p(z)$ be a polynomial of degree at most $n$. In this paper we obtain some new results about the dependence of$$\Bigg\|p(Rz)−\beta p(rz)+\alpha\Big\{\frac{R+1}{r+1}\Big)^n-|\beta|\Big\} p(rz)\Bigg\|_s$$ on $\|p(z)\|_s$ for every $\alpha$, $\beta \in C$ with $|\alpha| \leq 1$, $|\beta| \leq 1$, $R > r \ge 1$, and $s > 0$. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.

}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.02.006}, url = {http://global-sci.org/intro/article_detail/ata/4552.html} }
TY - JOUR T1 - $L^p$ Inequalities and Admissible Operator for Polynomials JO - Analysis in Theory and Applications VL - 2 SP - 156 EP - 171 PY - 2012 DA - 2012/06 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.02.006 UR - https://global-sci.org/intro/article_detail/ata/4552.html KW - $L^p$ inequality polynomials, Rouche’s theorem, admissible operator. AB -

Let $p(z)$ be a polynomial of degree at most $n$. In this paper we obtain some new results about the dependence of$$\Bigg\|p(Rz)−\beta p(rz)+\alpha\Big\{\frac{R+1}{r+1}\Big)^n-|\beta|\Big\} p(rz)\Bigg\|_s$$ on $\|p(z)\|_s$ for every $\alpha$, $\beta \in C$ with $|\alpha| \leq 1$, $|\beta| \leq 1$, $R > r \ge 1$, and $s > 0$. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.

M. Bidkham, H. A. Soleiman Mezerji & A. Mir. (1970). $L^p$ Inequalities and Admissible Operator for Polynomials. Analysis in Theory and Applications. 28 (2). 156-171. doi:10.3969/j.issn.1672-4070.2012.02.006
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