分担依赖于函数的常数亚纯函数正规族

Normal Families of Meromorphic Functions Concerning Sharing Constants Depending on Function

研究关于分担值的亚纯函数族的正规性,证明了如下结果:设k,n(≥k+3)是两个正整数,F为单位圆盘Δ内的一族亚纯函数,如果对于每一个f∈F,f的零点重级≥k,且存在仅依赖于f的非零有穷复数bf,cf满足:bf/cf是一个常数;min{σ(0,bf),σ(0,cf),σ(bf,cf)}≥m,这里m>0;对于每一对f,g∈F,有f(k)-1/bfn-1fn=cfg(k)-1/bgn-1gn=cg,那么F在Δ内正规.

Let κ and n （≥ k ＋ 3） be two positive integers, and f be a family of meromorphic functions in unit disk △. If for each function f∈f all zeros of f have multiplicity k at least,andthere exist nonzero finite complex numbers b f, Cf depending on f satisfying, b/Cf is a constant; min {σ（0,bf）,σ（0,cf）,σ（bf,cf）}≥m,for some m〉0g∈F;f（k）-1/bfn-1fn=cfg（k）-1/bgn-1gn=cg,for eachf,g∈f.Then f is normal in △.