Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301Growth estimate for rational functions with prescribed poles and restricted zeros247252547410.22075/ijnaa.2021.23465.2544ENIshfaq AhmadDarDepartment of Mathematics, University of Kashmir, Srinagar-190006, IndiaNisar AhmadRatherDepartment of Mathematics, University of Kashmir, Srinagar-190006, IndiaMohd ShafiWaniDepartment of Mathematics, University of Kashmir, Srinagar-190006, IndiaJournal Article20210120Let $r(z)= f(z)/w(z)$ 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.https://ijnaa.semnan.ac.ir/article_5474_3656cfa70e2a244467593adf62ee44b7.pdf