Normal Family Of Meromorphic Functions

In this paper we study the normality of families of meromorphic functions,whi- ch is an important subject in complex analysis.Much fruitful research work have been made by many scholars at home and abroad on this respect.The normal criteria ccocernning exceptional function and shared value is an important and interesting issue.This article is divided into three parts to discuss these issues.In part 1, we introduce the research background and the present research situati- on of the normal families of meromorphic functions and give the main results of this article.In part 2,we state some usual notations and basic results in value distribution theory and normality theory of meromorphic functions.In part 3,we discuss the normal criteria of meromorphic function.In section 1,we discuss the normal criteria concerning differential polynomial. The results obtained in the dissertation theorem 3.1.1 and theorem 3.1.2 perfect and generalize the present conclusions.In section 2,we discuss the normal criteria concerning exceptional function,and romote a normal criteria concerns exceptional value to the exceptional function situation and obtain theorem 3.2.1 and theorem 3.2.2.In section three,we discuss the normal criteria concerning shared value,study the situation of meromorphic functions with multiple zeros wchich have shared value with their derivatives,and obtain theorem 3.3.1,theorem 3.3.2 and theorem 3.3.2.