1Institute of Mathematics School of Mathematics Nanjing Normal University Nanjing 210046, P.R. China 2Department of Mathematics Changshu Institute of Technology Changshu, Jiangsu, 215500, P.R. China
Annales Polonici Mathematici, Tome 102 (2011) no. 1, pp. 91-99
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 $D$.
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
Affiliations des auteurs :
Yan Xu
1
;
Jianming Chang
2
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
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author = {Yan Xu and Jianming Chang},
title = {Normality criteria and multiple values {II}},
journal = {Annales Polonici Mathematici},
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doi = {10.4064/ap102-1-9},
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Yan Xu; Jianming Chang. Normality criteria and multiple values II. Annales Polonici Mathematici, Tome 102 (2011) no. 1, pp. 91-99. doi: 10.4064/ap102-1-9
