科研之友
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摘要
Let F be a family of meromorphic functions in a plane domain D, and a and b be finite non-zero complex values such that a/b is not an element of N \ {1}. If for every f is an element of F, f(z) = a double right arrow f'(z) = a and f'(z) = b double right arrow f ''(z) = b, then F is normal. We also construct a non-normal family F of meromorphic functions in the unit disk Delta = {vertical bar z vertical bar < 1} such that for every f is an element of F, f(z) = m 1 double left right arrow f'(z) = m 1 and f'(z) = 1 double left right arrow f ''(z) = 1 in Delta, where m is a given positive integer. This answers Problem 5.1 in the works of Gu, Pang and Fang.
- 出版日期2009-8
- 单位常熟理工学院
