Normality and Quasinormality of Zero-free Meromorphic Functions  

作　　者：Jian Ming CHANG 

机构地区：[1]Changshu Institute of Technology, Department of Mathematics

出　　处：《Acta Mathematica Sinica,English Series》2012年第4期707-716,共10页数学学报（英文版）

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

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.

关 键 词：Meromorphic functions normal family 

分 类 号：O174.52[理学—数学] O152.1[理学—基础数学]