Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Normal families of meromorphic functions sharing values or functions | Jiang and Gao Journal of Inequalities and Applications 2011 2011 72 http content 2011 1 72 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Normal families of meromorphic functions sharing values or functions Yunbo Jiang and Zongsheng Gao Correspondence jiangyunbo@ss. School of Mathematics and Systems Science and LMIB Beihang University Beijing 100191 People s Republic of China Springer Abstract In this paper we investigate the normal families of meromorphic functions concerning shared values and shared analytic functions and prove some normal criteria that generalize or extend some results obtained by Q. C. Zhang Y. T. Li and Y. X. Gu J. M. Chang. Mathematics Subject Classification 2000 30D45 30D35. Keywords meromorphic function holomorphic function shared value shared analytic function L. Yang s inequality normal family 1. Introduction and main results The notations and concepts used in this paper can be found in 1-3 . In this paper We also use fz a g z b to stand for g z b when fz a. Let D be a domain in the complex plane C F be a family of meromorphic functions defined in D. F is said to be normal in D in the sense of Montel if every sequence fn z e F n 1 2 . has a subsequence fnk z k 1 2 . that converges spherically locally uniformly in D to a meromorphic function or see 2 4 5 . In 1998 Y. F. Wang and M. L. Fang 6 proved the following theorem. Theorem A. Let F be a family of meromorphic functions in D n k e N with n k 2. If for every function f e F f has only zeros of order at least n and f k 1 then F is normal in D. In 2004 M. L. Fang and L. Zalcman 7 proved the following theorem. Theorem B. Let F be a family of meromorphic functions in D and n be a positive integer. If for each pair of functions f and g in F f and g share the value 0 and f f and gn g share a non-zero value b in D then F is normal in D. In 2008 Q. C. Zhang 8 proved the following Theorems C and D .
