Normality criteria for families of zero-free meromorphic functions
Volume 115 / 2015
Annales Polonici Mathematici 115 (2015), 89-98
MSC: Primary 30D45; Secondary 30D35.
DOI: 10.4064/ap115-1-7
Abstract
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.
