In this paper, we deal with the problem of uniqueness of rr~rorrorphic functions. It is shown that there exist two finite sets Sj (j= 1, 2) such that any two nonconstant merorrorphic functions f and g satisfying Ef(Sj)=Eg(Sj) for j=l, 2 must be identical, which answers a question posed by Gross.

This paper studies the problem of uniqueness of entire functions that share real zeros and real ones. An example is provided to show that a result of Czubiak and Gundersen is not completely correct. Results in this paper correct the result of Czubiak and Gundersen, and also correct a result of Osgood and Yang.

This paper studies the problem of uniqueness of meromorphic functions and shows that there exist two finite setsSj (j=1, 2) such that any two nonconstant meromorphic functions f and g satisfying Ef (Sj)=Eg (Sj) for j=1, 2 must be identical. The results in this paper improve some theorems given by Nevanlinna7, Brosch8, Yi6 and other authors. As a special case, these results answer an open question posed by Gross5.

In this paper, we show that if two non-constant meromorphic functions f and g satisfy E(aj; k; f)=E(aj; k;g) for j = 1; 2;:::; 5, where aj are live distinct small functions with respect to f and g, and k is a positive integer or 1 with k 14, then f g. As a special case this also answers the longstanding problem on uniqueness of meromorphic functions concerning small functions.