TY - JOUR
T1 - $L^p$ Inequalities and Admissible Operator for Polynomials
AU - M. Bidkham, H. A. Soleiman Mezerji & A. Mir
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 - <p style="text-align: justify;">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 $|\alpha| \leq 1$, $|\beta| \leq 1$, $R &gt; r \ge 1$, and $s &gt; 0$. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.</p>