@article {
author = {Dar, Ishfaq and Rather, Nisar and Wani, Mohd},
title = {Growth estimate for rational functions with prescribed poles and restricted zeros},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {13},
number = {1},
pages = {247-252},
year = {2022},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {},
doi = {10.22075/ijnaa.2021.23465.2544},
abstract = {Let $r(z)= f(z)/w(z)$ where $f(z)$ be a polynomial of degree at most $n$ and $w(z)= \prod_{j=1}^{n}(z-a_{j})$, $|a_j|> 1$ for $1\leq j \leq n.$ If the rational function $r(z)\neq 0$ in $|z|< k$, then for $k =1$, it is known that $$\left|r(Rz)\right|\leq \left(\frac{\left|B(Rz)\right|+1}{2}\right) \underset{|z|=1}\sup|r(z)|\,\,\, for \,\,\,|z|=1$$ where $ B(z)= \prod_{j=1}^{n}\left\{(1-\bar{a_{j}}z)/(z-a_{j})\right\}$. In this paper, we consider the case $k \geq 1$ and obtain certain results concerning the growth of the maximum modulus of the rational functions with prescribed poles and restricted zeros in the Chebyshev norm on the unit circle in the complex plane.},
keywords = {Rational functions,Polynomial Inequalities,Zeros},
url = {https://ijnaa.semnan.ac.ir/article_5474.html},
eprint = {https://ijnaa.semnan.ac.ir/article_5474_3656cfa70e2a244467593adf62ee44b7.pdf}
}