Normal Families of Meromorphic Functions and Shared Set  

作　　者：TIAN Hong-gent CHEN Weit YUAN Wen-jun 

机构地区：[1]School of Mathematics Science, Xinjiang Normal University, Urumqi 830054, China [2]School ofMathematics and Information Science, Guangzhou University, Guangzhou 510006, China

出　　处：《Chinese Quarterly Journal of Mathematics》2015年第2期159-165,共7页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China（l1461070, 11271090）; Supported by the Natural Science Foundation of Guangdong Province（S2012010010121）

摘　　要：In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m > 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related resultsIn this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying（i） bf/cf is a constant;（ii） min{σ（0,bf）,σ（0,cf）,σ（bf,cf）} ≥m for some m 〉 0;（iii） Ef＇（Sf） Ef（Sf）,where Sf = {bf,cf}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and

关 键 词：meromorphic function shared set normal family 

分 类 号：O174.5[理学—数学]