Abstract:
In this paper, we study the normality of holomorphic functions and prove the following results: Let
M, n, k be three positive integers satisfying
M≥9 when
n=k=1 and
when
nk>1, b(≠0) , is a finite complex number; let F be a family of holomorphic functions in a domain D and H(f) be a differential polynomial of f and satisfy
, if for each f
∈ F , satisfies (1) all zeros of f have multiplicity at least k; (2) all zeros of
f(n)f(k)+H(f)-b have multiplicity
≥M , then F is normal in
D .