【摘要】 文章证明了若F为区域D内一族亚纯函数,其每个函数的零点重数至少为k+l,l≥2,k为正整数,若对f∈F有:f(k)(z)=0f(k+l)(z)=0,f(k+l)(z)=b→f(k)(z)=b则F在区域D内正规,其中b≠0.若F={f(z)}为区域D内一族亚纯函数,F(k)(z)={f(k)(z)|f(z)∈F},若对f(z)∈F有f(z)的零点重数至少为k,且存在常数A≥1,使得f(z)=0→|f(k)(z)|≤A,则当F(k)在D上正规时,F也正规.更多还原

【Abstract】 This paper proves the following theorem:Let F be a family of meromorphic functions in a domain D,k and l≥2 be positive integers,and b a non-zero complex number. If for each f∈F,the zeros of f(z)are of multiplicity at least k+l,and f(k)(z)=0f(k+l)(z)=0,f(k+l)(z)=b→f(k)(z)=b,then F is normal in D. any family F of meromorphic functions in a domain, whose every member’s zeros are of multiplicity at least k and the member’s k-order derivative takes values at the zeros with a uniform finite boundary,will be normal if the family consisted of the k-order derivatives of all member’s of F is normal.更多还原