Shared Values And Normal Families

The thesis aims to the normality of families of meromorphic functions,which is an important subject in complex analysis.Much fruitful research on this respect has been made by many scholars at home and abroad .The normal criteria concerning shared value is an important and interesting issue.The thesis is divided into three parts,as followings,The first part is an introduction,which includes the background of relevant research and the present research situation of this research ,It also give the main results of this thesis.The second part states some usual notations and basic results in value distribution theory of meromorphic functions, normality theory and normality theory concerning shared value.The third part discusses the normal criteria of meromorphic functions.In section one,by discussing the normal criteria concerning shared value,The author mainly study the situation of meromorphic functions which have shared value with their derivatives.Through this study, theorem 3.1.1, theorem 3.1.2, theorem 3.1.3and theorem 3.1.4.are obtained.In section two,the normal problem of derivative family of meromorphic functions is studied.For the mormal family of meromorphic functions,the number of elements of sharing set is needed at least 3,but for the normal family of derivatives the number of that is only needed 2.It is proved that a family of k-th derivatives of meromorphic functions in domain is normal if all functions of the derivatives family share a set S which has only two elements ,Theorem 3.2.1and theorem 3.2.2 are the results of this section.