摘要
Let k, K ∈1N and F be a family of zero-free meromorphic functions in a domain D such that for each f ∈ F, f（k） - 1 has at most K zeros, ignoring multiplicity. Then F is quasinormal of order at most v=k/k＋1,where v is equal to the largest integer not exceeding k/k＋1.In particular, if K = k, then F is normal. The results are sharp.
Let k, K ∈1N and F be a family of zero-free meromorphic functions in a domain D such that for each f ∈ F, f（k） - 1 has at most K zeros, ignoring multiplicity. Then F is quasinormal of order at most v=k/k＋1,where v is equal to the largest integer not exceeding k/k＋1.In particular, if K = k, then F is normal. The results are sharp.
基金
Supported by National Natural Science Foundation of China(Grant No.10871094)
NSFU of Jiangsu,China(Grant No.08KJB110001)
Qinglan Project of Jiangsu,China,and SRF for ROCS,SEM
