NORMAL FAMILIES AND SHARED VALUES OF HOLOMORPHIC FUNCTIONS  

作　　者：Li Jiangtao Yi Hongxun 

机构地区：[1]Department of Mathematics, Shandong University, Shandong 250100, China [2]Department of Mathematics, Chongqing University, Chongqing 400044, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2006年第3期335-342,共8页高校应用数学学报（英文版）（B辑）

基　　金：The first author is supported in part by the Post Doctoral Fellowship at Shandong University.The second author is supported by the national Nature Science Foundation of China (10371065).

摘　　要：Let F be a family of holomorphic functions in a domain D, k be a positive integer, a, b（≠0）, c（≠0） and d be finite complex numbers. If, for each f∈F, all zeros of f-d have multiplicity at least k, f^（k） = a whenever f=0, and f=c whenever f^（k） = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp.Let F be a family of holomorphic functions in a domain D, k be a positive integer, a, b（≠0）, c（≠0） and d be finite complex numbers. If, for each f∈F, all zeros of f-d have multiplicity at least k, f^（k） = a whenever f=0, and f=c whenever f^（k） = b, then F is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp.

关 键 词：holomorphic function normal family shared value. 

分 类 号：O17[理学—数学]