On the uniqueness of meromorphic functions that share four values in one angular domain

Abstract

The main purpose of this paper is to investigate the uniqueness of transcendental meromorphic functions that share four values in one angular domain which is an unbounded subset of the whole complex plane. From one of our main results, a question of J.H. Zheng [J.H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domain, Complex Var. Elliptic Equ. 48 (9) (2003) 777–785] is completely answered. Furthermore, we give an example to explain the necessity of the condition lim r → ∞ S α , β ( r , f ) log ( r T ( r , f ) ) = ∞ in our results.