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.

In this paper, we deal with the relation between the characteristic functions of meromorphic functions that share three values CM. As applications of our main results, we shall a rmatively settle two conjectures proposed by Mues and Osgood-Yang.

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.

In this paper, we prove a result on uniqueness of meromorphic functions sharing three values counting multiplicity. As applications of this, many known results can be improved. Examples are provided to show that the results in this paper are best possible