涉及复合函数分担条件的全纯函数正规族  

Normal Families of Holomorphic Functions Concerning Shared Conditions of Composite Functions

作　　者：黄小杰 刘芝秀[2] 李运通[3] HUANG Xiaojie;LIU Zhixiu;LI Yuntong(School of Computer Science,Fudan University,Shanghai 200433,China;School of Science,Nanchang Institute of Technology,Nanchang 330099,China;Dean＇s Office,Shaanxi Railway Institute,Weinan 714000,China)

机构地区：[1]复旦大学计算机科学技术学院,上海200433 [2]南昌工程学院理学院,江西南昌330099 [3]陕西铁路工程职业技术学院教务处,陕西渭南714000

出　　处：《杭州师范大学学报（自然科学版）》2018年第6期641-645,672,共6页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671091;11771090);陕西省教育厅专项基金项目(17JK0170)

摘　　要：讨论了涉及复合函数分担条件的全纯函数正规族,提出了"局部度"的概念,利用Pang-Zalcman方法和Nevanlinna理论证明了:对于区域D上的全纯函数族!,若P(z)是次数为n的多项式,φ(z)是局部度小于n的解析函数,且对任意f,g∈F,满足P(f)和P(g)在D上IM分担φ(z),则!是D上的正规族.并举例说明了该结论中局部度条件不能减弱,在特定意义下是最优的.The normal families of holomorphic functions concerning shared conditions of composite functions are discussed. The concept of ‘local degree’ is proposed. And it is proved by Pang-Zalcman method and Nevanlinna theory that for a family of holomorphic functions F defined on domain D , if P（z） be a polynomial with degree of n , φ（z） be an analytic function with local degree less than n , and for any f,g∈ F , P（f） and P（g） IM share φ（z） on domain D , then F be a normal family. The examples are provided to show that the condition related local degree can not be weakened, in a sense, is the best possible.

关 键 词：正规族 分担函数 复合函数 

分 类 号：O174.52[理学—数学]