Some inequalities for the growth of rational functions with prescribed poles

	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
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
آمار تعداد مشاهده مقاله: 17,742 تعداد دریافت فایل اصل مقاله: 12,633

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