一族全纯函数的正规定则

Normality of a family of holomorphic functions

研究了区域D内的全纯函数族F的正规性 ,给出了T(r ,f)的一个上界 ,得到了全纯函数族F正规的一个充分条件 .证明了当F中有一个函数 f在D内满足f(z)·f′(z) ≠β时 。

Normality of a family F of holomorphic functions in a region D is discussed. An upper boundary of the quantity T(r,f) is given. A sufficient condition for the family F to be normal is obtained and it is proved that if f(z). f′(z)≠β for all f F and every z in D then F is normal.