分担连续函数的全纯函数正规族

Normal Families of Holomorphic Functions Sharing Continuous Function

研究了分担连续函数的全纯函数族的正规性问题,推广了一些已有的结论.设F为定义在区域D上的全纯函数族,h1,h2为两个连续函数满足对_z∈D有h1(z)≠h2(z),并设k≥2为正整数.若f∈F,有f(z)=hi(z)=〉|f(k)(z)|≤|hi(z)|,i=1,2,则F为D上的正规族;并举例说明了k=1时,结论不成立.此外,还将分担值条件用拓扑度条件代替得到了一个涉及拓扑度条件的全纯函数族正规定则.

It studies the normality of family of holomorphic functions sharing continuous function and extends some existing conclusions. Let F be a family of holomorphic functions defined on domain D,h1,h2 be two different continuous functions satisfied z∈D,h1（ z） ≠h2（ z）,and k≥2 be a positive integer. If f∈F,such that f（ z） = hi（ z） =〉 ｜ f（ k）（ z） ｜ ≤ ｜ hj（ z） ｜,i = 1,2,then F is a normal family; An example is given to explain that the conclusion does not hold when k = 1.In addition,a normal criterion concerning topological degree is also got by replacing shared value condition with topological degree condition.