A normal criterion concerning zero numbers

Abstract Let %$n \ge 4%$ be a positive integer, %$\mathcal {F}%$ be a family of meromorphic functions in D and let %$a(z)(\not \equiv 0), b(z)%$ be two holomorphic functions in D. If, for any function %$f \in \mathcal { F}%$, (1)%$f(z) \ne \infty %$ when %$a(z)=0%$, (2) %$f'(z)-a(z)f^{n}(z)-b(z...
Ausführliche Beschreibung

Abstract Let %$n \ge 4%$ be a positive integer, %$\mathcal {F}%$ be a family of meromorphic functions in D and let %$a(z)(\not \equiv 0), b(z)%$ be two holomorphic functions in D. If, for any function %$f \in \mathcal { F}%$, (1)%$f(z) \ne \infty %$ when %$a(z)=0%$, (2) %$f'(z)-a(z)f^{n}(z)-b(z)%$ has at most one zero in D, then %$\mathcal {F}%$ is normal in D. Ausführliche Beschreibung