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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Some normality criteria of functions related a Hayman conjecture | Yuan et al. Journal of Inequalities and Applications 2011 2011 97 http www.journalofinequalitiesandapplications.eom content 2011 1 97 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Some normality criteria of functions related a Hayman conjecture Wenjun Yuan1 Bing Zhu2 and Jianming Lin3 Correspondence wjyuan1957@126.com ljmguanli@21cn.com 1School of Mathematics and Information Science Guangzhou University Guangzhou 510006 China 3School of Economic and Management Guangzhou University of Chinese Medicine Guangzhou 510006 China Full list of author information is available at the end of the article Springer Abstract In the article we study the normality of families of meromorphic functions concerning shared values. We consider whether a family meromorphic functions F is normal in D if for every pair of functions f and g in F f f and gn g share a nonzero value a. Two examples show that the conditions in our results are best possible in a sense. 1 Introduction and main results Letfz and g z be two nonconstant meromorphic functions in a domain D C and let a be a finite complex value. We say that f and g share a CM or IM in D provided that f - a and g - a have the same zeros counting or ignoring multiplicity in D. When a the zeros off - a means the poles off see 1 . It is assumed that the reader is familiar with the standard notations and the basic results of Nevanlinna s value-distribution theory 1-4 . Bloch s principle 5 states that every condition which reduces a meromorphic function in the plane C to be a constant forces a family of meromorphic functions in a domain D normal. Although the principle is false in general see 6 many authors proved normality criterion for families of meromorphic functions corresponding to Liouville-Picard type theorem see 4 . It is also more interesting to find normality criteria from the point of view of shared values. In this area Schwick 7 first proved an interesting result that a family of .
