Normality criteria for families of zero-free meromorphic functions

Jun-Fan Chen¹

¹ Department of Mathematics Fujian Normal University Fuzhou 350117, Fujian Province, P.R. China

Annales Polonici Mathematici, Tome 115 (2015) no. 1, pp. 89-98.

Résumé

Let $\mathcal F$ be a family of zero-free meromorphic functions in a domain $D$, let $n$, $k$ and $m$ be positive integers with $n\geq m+1$,\vadjust {\vskip 1pt} and let $a\not =0$ and $b$ be finite complex numbers. If for each $f\in \mathcal F$, $f^m+a(f^{(k)})^n-b$ has at most $nk$ zeros in $D$, ignoring multiplicities, then $\mathcal F$ is normal in $D$. The examples show that the result is sharp.

Détail

DOI : 10.4064/ap115-1-7

Keywords: mathcal family zero free meromorphic functions domain positive integers geq vadjust vskip finite complex numbers each mathcal f n b has zeros ignoring multiplicities mathcal normal examples result sharp