On the Existence of T-Direction and Nevanlinna Direction of K-Quasi-Meromorphic Mapping Dealing with Multiple Values

In this paper, by using Ahlfors theory of covering surfaces, we prove that for quasi-meromorphic mapping f satisfying lim sup r→∞ T(r; f)/(log r)²= +∞; there exists at least one T-direction of f dealing with multiple values. We also prove that there exists at least one Nevanlinna direction of f dealing with multiple values which is also T-direction of f dealing with multiple values under the same condition.