Meromorphic Functions That Share One Finite Value CM or IM with Their First Derivative

In this paper we shall prove that if a non-constant meromorphic function f and its derivative ƒ' share the value a(= 0,æ) cm (im) and if n^(r ,1/f)= s (r ,f) n^(r,1/f)+n^(r,1/f')=s(r,f)then either f=f' or f (z)=a(z-c)/1+ae^-z f(z)=2a/1-ae^-2z where a(6= 0) and c are constants. these results give improvement and.extension of the following result of gundersen: if a non-constant meromorphic function f and its derivative f' share two distinct values 0, a(6=æ) cm, then f = f'.