亚纯函数分担集合的正规定则

Normality Concerning Meromorphic Functions and Shared Set

讨论了亚纯函数分担集合的正规定则,主要结果为:设是区域D内的一族亚纯函数,a,b和c是三个有限复数,且a≠b,k和q是两个正整数,令S=﹛a,b﹜。若对任意的f∈ ,满足:1) ?z∈D,h(f(k)(z))∈S?f(z)∈S,其中ai(z)(i=1,2,…,q-1)是全纯函数,h(f(k)(z))=(f(k)(z))q+aq-1(z)(f(k)(z))q-1+…+a1(z)f(k)(z);2) f-c的零点重级至少为k+1,则 在D内正规。

The normal family of meromorphic functions concerning shared set was studied.The following result was proved:Let be a family of meromorphic functions in a domain D,a,b and c be three finite complex numbers,where a≠b,k and q be two positive integers,let S=﹛a,b﹜.If for each f∈, 1)?z∈D,h(f(k)(z))∈S?f(z)∈S, where ai(z)(i=1,2,…,q-1)is holomorphic function and h(f(k)(z))=(f(k)(z))q+aq-1(z)(f(k)(z))q-1+…+a1(z)f(k)(z);2)f-c have zeros with multiplicities at least k+1,then is normal in D.