Normality Of Meromorphic Functions With Shared Values

In1907, P. Montel introduced the conception of normal family. The theory ofnormal family has an ample development since it not only plays a significant role inthe basic research, but also its own important applications. Nearly these years, manymathematicians find the new normal criterion according Bloch principle and someproblems on value distribution.In this paper, we study the problems of normal families concerning shared valuesand shared functions, and obtain some normal criterion. This paper carries out thefollowing tasks.The first chapter of this paper is about preliminary theorem, and the backgroundand the meaning of normal family are introduced.In the second chapter, we briefly introduce some basic definitions and significantresults in value distribution.In the third chapter, we mainly some conceptions and basic theorems of normalfamily.In the fourth chapter, we mainly study the normality of meromorphic functionsaboutf (k) afnandg (k) agnshare a constant b, which improve or generalize theprevious theorems, meanwhile, some examples are given to show the sharpness of ourresults.In the fifth chapter, we mainly discuss aboutff (k)andgg (k)share an analyticfunction (z).