Growth estimate for rational functions with prescribed poles and restricted zeros | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 13، شماره 1، خرداد 2022، صفحه 247-252 اصل مقاله (338.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23465.2544 | ||
| نویسندگان | ||
| Ishfaq Ahmad Dar* ؛ Nisar Ahmad Rather؛ Mohd Shafi Wani | ||
| Department of Mathematics, University of Kashmir, Srinagar-190006, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Rational functions؛ Polynomial Inequalities؛ Zeros | ||
| مراجع | ||
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