【摘要】 作者证明了以下命题:设F={f}为整函数族,每个函数f∈F,f的零点重数至少为k.又a1(z),a2(z),…,ak(z)为k个整函数.记h(z)=f(k)(z)+a1(z)f(k-1)(z)+…+ak(z)f(z).则若对于区域D内任意点z,有h(z)≠0,|h(z)|<1,且复合函数族{h(f(z))|f(z)∈F}在区域D内正规,则整函数族F在D内正规,并得到涉及齐次微分多项式的整函数族相应的正规定则,推广了已有结果.更多还原

【Abstract】 In this paper,the authors obtain the following normal criterion:Let F={f} be a family of entire functions,all of whose zeros have multiplicity k at least,and a₁（z）,a₂（z）,…,a_k（z）be entire functions.Setting h（z）=f^（k）（z）+∑ki=1a_i（z）f^（k-i）（z）,h（z）≠0,and |h（z）|<1,if {h（f（z））|f∈F} is normal on D,then F also is normal on D,where k is positive number.Finally,they find that the conclusion also hold for a family of holomorphic functions related to homogeneous differential polynomial of degree q with entire functions coefficient a_j（z）,j=1,2,…,p about f,f′,f″,…,f^（k-1）.更多还原