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Some inequalities for the growth of rational functions with prescribed poles | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 55، دوره 14، شماره 1، فروردین 2023، صفحه 717-722 اصل مقاله (331.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27564.3652 | ||
| نویسندگان | ||
| Nisar Ahmad Rather؛ Mohmmad Shafi Wani؛ Aijaz Ahmad Bhat* | ||
| Department of Mathematics, University of Kashmir, Srinagar-190006, India | ||
| تاریخ دریافت: 31 خرداد 1401، تاریخ بازنگری: 03 شهریور 1401، تاریخ پذیرش: 04 شهریور 1401 | ||
| چکیده | ||
| Let $\mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-\beta_j)$, $|\beta_j|>1$ for $1\leq j\leq n$. In this paper, we prove some results concerning the growth of rational functions with prescribed poles by involving some of the coefficients of polynomial $f(z)$. Our results not only improve the results of N. A. Rather et al. [8], but also give the extension of some recent results concerning the growth of polynomials by Kumar and Milovanovic [3] to the rational functions with prescribed poles and we obtain the analogous results for such rational functions with restricted zeros. | ||
| کلیدواژهها | ||
| Rational functions؛ polynomials؛ inequalities | ||
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