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Normal families and shared values of meromorphic functions

Tom 80 / 2003

Annales Polonici Mathematici 80 (2003), 133-141 MSC: Primary 30D45. DOI: 10.4064/ap80-0-11

Streszczenie

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 $b\not =(m+1)d,$ $m=1,2,\dots .$

Autorzy

• Mingliang FangDepartment of Mathematics
Nanjing Normal University
Nanjing 210097, P.R. China
e-mail
• Lawrence ZalcmanDepartment of Mathematics and Statistics
Bar-Ilan University
52900 Ramat-Gan, Israel
e-mail

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