Small Functions of Meromorphic Functions that Share Three Values GCM

Abstract

Abstract. In this paper, we deal with the problem of uniqueness of meromorphic func-tions that share three values, and obtain some theorems which improve some results ofBrosch, Yi and other authors. 1. Introduction and de nitionsLet fand gbe two nonconstant meromorphic functions on the open complexplane C, and let abe a nite value in the complex plane. We say that fand gsharethe value aCM ( IM ) provided that f aand g ahave the same zeros countingmultiplicities ( ignoring multiplicities ), and f;gshare 1CM ( IM ) provided that1=f; 1=gshare 0 CM ( IM ). We do not explain the standard notations of valuedistribution theory as those are available in Hayman [4] or Yang and Yi [11].We denote by S(r;f) any function satisfying S(r;f) = o(T(r;f)) as r!+1possibly outside a set Eof nite Lebesgue measure. A meromorphic function a(z)is said to be a small function of f, if T(r;a) = S(r;f):Let fand gbe nonconstant meromorphic functions and abe a small meromor-phic function of fand g. We denote by N(r;a;f;g)( and N