Geodesic
Growth Estimate for Rational Functions with Prescribed Poles and Restricted Zeros
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 2, p. 305

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 $w(z) = \prod_{j=1}^{n}(z-a_j)$, $|a_j|>1$ for $1\leq j\leq n$. In this paper, we extend some famous results concerning to the growth of polynomials by T. J. Rivlin, A. Aziz and others to the rational functions with prescribed poles and thereby obtain the analogous results for such rational functions with restricted zeros.
Classification : 26D10, 41A17, 30C15
Keywords: rational functions, polynomial inequalities, growth, zeros 
N. A. Rather; M. Shafi; Ishfaq Dar. Growth Estimate for Rational Functions with Prescribed Poles and Restricted Zeros. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 2, p. 305 . http://geodesic.mathdoc.fr/item/KJM_2025_49_2_a8/
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