Normality criteria and multiple values II
Tom 102 / 2011
Annales Polonici Mathematici 102 (2011), 91-99
MSC: Primary 30D05; Secondary 30D45.
DOI: 10.4064/ap102-1-9
Streszczenie
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 $D$.
