부산대학교 도서관

Three theorems are given whereby complex numbers $a$ and $b$ in known results are replaced by analytic functions. One result assumes $a(z)\nequiv 0$ and $d(z)$ are analytic functions in a domain $D$ and $F$ is a family of meromorphic functions in $D$. If for every $f$ in $F$ $$f'(z)-a(z)(f(z))^2\neq d(z)$$ the poles of $f$ are of multiplicity greater than or equal to 4, and $f(z)\neq\infty$ when $a(z)=0$, then $F$ is a normal family in $D$. An example shows $f(z)\neq\infty$ when $a(z)=0$ is a necessary condition for the theorem. The result extends work of M. L. Fang\ and W. J. Yuan\ [Indian J. Math. {\bf 43} (2001), no.~3, 341--351; MR1880489 (2002m:30040)].