Normal Criterion Concerning Shared Values

Abstract

We study normal criterion of meromorphic functions shared values, we obtain the following. Let $F$ be a family of meromorphic functions in a domain $D$, such that function $f\in F$ has zeros of multiplicity at least 2, there exists nonzero complex numbers $b_f,c_f$ depending on $f$ satisfying $(\text{i})b_f/c_f$ is a constant; $(\text{i}\text{i})\min \hspace{0.17em}\{\sigma (0,b_f),\sigma (0,c_f),\sigma (b_f,c_f)\ge m\}$ for some $m>0$; $(\text{i}\text{i}\text{i})(1/c_f^{k-1})(f^{\prime }{)}^k(z)+f(z)\ne b_f^k/c_f^{k-1}$ or $(1/c_f^{k-1})(f^{\prime }{)}^k(z)+f(z)=b_f^k/c_f^{k-1}\Rightarrow f(z)=b_f$, then $F$ is normal. These results improve some earlier previous results.