全纯函数族涉及公共值的正规定则

Normal criteria of holomorphic functionfamilies concerning shared values

研究涉及公共值的全纯函数正规族问题.设F为单位圆△内的全纯函数族,a,b为两个判别的有穷复数且b≠0.文中证明了若对每一个f∈F,Ef(a)=Ef′(a),Ef′(b) Ef(b),则F在单位圆△内正规.

In this paper the problem of normal families of holomorphic functions with relation to shared values has been researched,and the following result is proved:Let F be a family of holomorphic functions in unit disc △,and a,b be two distinct finite complex values such that b≠0.If for every f∈F,E_f(a)=E_{f′}(a),_{f′}(b)_f(b),then F is normal in △.