Normalities Invole Shared Functions And Omitted Functions

Let F be a family of holomorphic functions in the plain domain D , k is a positive integer, a₁(z) and a₂(z) are two holomorphic functions in the plain domain D , and |a₁(z)|² + |a₂(z)|²â‰ 0 . If for every f(z)∈F, the zeros of f(z) are of multiplicity at least k , f(z)=0(?)|f^(k)|≤M, (constant M≥0) and f(z)=a_i(z)(?)f^(k)=a_i(z), i=1,2. then F is normal in D.Let F be a family of holomorphic functions in the plane domain D, k is a positive integer and k≥2.All of whose zeros have multiplicity of k , and satisfying the conditionf(z)=0(?)|f^(k)(z)|<|z|,f^(k)(z)≠z,Then F is normal in D.