Document Type : Research Paper

Authors

• Nisar Ahmad Rather
• Mohmmad Shafi Wani
• Aijaz Ahmad Bhat

Department of Mathematics, University of Kashmir, Srinagar-190006, India

Abstract

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 $1\le j\le n$. 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.

Keywords

• Rational functions
• polynomials
• inequalities