Unicity theorems for meromorphic functions that share three values

This paper studies the problem of the uniqueness of meromorphic functions that share three values.The results in this paper improve some theorems given by H. Ueda, Shou-Zhen Ye and Hong-Xun Yi.Examples are provided to show that our results are sharp.H. Ueda proved the following theorem.THEOREM A (see [3]).Let f and g be two distinct nonconstant entire functions such that f and g share 0, 1 CM., and let a be a finite complex number, and aφO, 1. // a is lacunary for f, then 1-a is lacunary for g, andIn [4] the present author proved the following result which is an improvement of the above result.THEOREM B. Let f and g be two distinct nonconstant entire functions such that f and g share 0, 1 CM., and let a be a finite complex number, and aφQ, 1.