涉及亚纯函数微分多项式和分担值的正规函数

研究亚纯函数的微分多项式与分担值的关系,得到了一族新的正规函数,即:设F是定义在单位圆盘上的一族亚纯函数,零点重级至少为k并且存在正数A≥1,使得当f(z)=0时有f(k)(z)≤A.f的微分多项式为F(z),如果对于任意的f∈F,有f(z)∈{a,b}F(z)∈{a,b},这里a,b是2个互异的非零有穷复常数,则存在仅与a,b有关的正数M,使得对于每个f∈F,有(1-∣z∣)2∣f′(z)∣f 1+∣f(z)∣2≤M

Normal function concerning differential polynomial in meromorphic functions and shared values

Mainly studied the connection between the differential polynomial in meromorphic functions and shared values,and obtained a new normal function.Let F be a family of meromorphic functions on the plain domain D,all of whose zeros have multiplicity at least k and there exists a positive numberA≥ 1,such thatf(k)(z) ≤ A whenever f(z) =0,f ∈ F.WriteF(z) as a differential polynomial inf(z),and then if for anyf ∈ F,f(z)∈{a,b}F(z)∈{a,b},where a,b are two distinct finite nonzero complex numbers,then there exists a positive numberM =M(a,b),such that for everyf ∈ F,(1-∣z∣)2∣f′(z)∣f 1+∣f(z)∣2≤M where M only depends ona and b.