Normal families and shared values of meromorphic functions
Volume 80 / 2003
Annales Polonici Mathematici 80 (2003), 133-141
MSC: Primary 30D45.
DOI: 10.4064/ap80-0-11
Abstract
Let ${\cal F}$ be a family of meromorphic functions on a plane domain $D,$ all of whose zeros are of multiplicity at least $k\ge 2.$ Let $a$, $b$, $c$, and $ d$ be complex numbers such that $d\not =b,0$ and $c\not =a.$ If, for each $f\in {\cal F},$ $f(z)=a\Leftrightarrow f^{(k)}(z)=b$, and $f^{(k)}(z)=d\Rightarrow f(z)=c,$ then ${\cal F}$ is a normal family on $D.$ The same result holds for $k=1$ so long as $b\not =(m+1)d,$ $m=1,2,\dots .$
