Normality criteria and multiple values II

Yan Xu¹ ; Jianming Chang²

¹ Institute of Mathematics School of Mathematics Nanjing Normal University Nanjing 210046, P.R. China
² Department of Mathematics Changshu Institute of Technology Changshu, Jiangsu, 215500, P.R. China

Annales Polonici Mathematici, Tome 102 (2011) no. 1, pp. 91-99

Résumé

Let $\cal F$ be a family of meromorphic functions defined in a domain $D$, let $\psi$ $(\not\equiv 0, \infty)$ be a meromorphic function in $D$, and $k$ be a positive integer. If, for every $f\in \cal F$ and $z\in D$, (1) $f\neq 0$, $f^{(k)}\neq 0$; (2) all zeros of $f^{(k)}-\psi$ have multiplicities at least $(k+2)/k$; (3) all poles of $\psi$ have multiplicities at most $k$, then $\cal F$ is normal in $D$.

Détail

DOI : 10.4064/ap102-1-9

Keywords: cal family meromorphic functions defined domain psi equiv infty meromorphic function positive integer every cal neq neq zeros psi have multiplicities least poles psi have multiplicities cal normal