Year: 2012
Analysis in Theory and Applications, Vol. 28 (2012), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.3969/j.issn.1672-4070.2012.02.006
Analysis in Theory and Applications, Vol. 28 (2012), Iss. 2 : pp. 156–171
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: $L^p$ inequality polynomials Rouche’s theorem admissible operator.