Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Uniqueness of Meromorphic Functions with Multiple Values in Some Angular Domains | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 208516 10 pages doi 2009 208516 Research Article On Uniqueness of Meromorphic Functions with Multiple Values in Some Angular Domains Zu-Xing Xuan1 2 1 Department of Mathematical Sciences Tsinghua University Haidian District Beijing 100084 China 2 Department of Basic Courses Beijing Union University No. 97 Bei Si Huan Dong Road Chaoyang District Beijing 100101 China Correspondence should be addressed to Zu-Xing Xuan xuanzuxing@ Received 4 March 2009 Accepted 30 June 2009 Recommended by Narendra Kumar Govil This article deals with problems of the uniqueness of transcendental meromorphic function with shared values in some angular domains dealing with the multiple values which improve a result of J. Zheng. Copyright 2009 Zu-Xing Xuan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction A transcendental meromorphic function is meromorphic in the complex plane C and not rational. We assume that the readers are familiar with the Nevanlinna theory of meromorphic functions and the standard notations such as Nevanlinna deficiency ô a f of f z with respect to a e C and Nevanlinna characteristic Tfr f of f z . And the lower order p and the order 1 are in turn defined as follows . . log T r f u u f liminf w r MX log r 1 1f limsuplogl r f rMX iog r For the references please see 1 . An a e C C u i X is called an IM ignoring multiplicities shared value in X c C of two meromorphic functions f z and g z if in X f z a if and only if g z a. It is Nevanlinna 2 who proved the first uniqueness theorem called the Five Value Theorem which says that two meromorphic functions f z and g z are identical 2 Journal of Inequalities and Applications if they have five distinct IM shared values in X C. After
