Normality Concerning Shared Values Between two Families

Abstract

We improve a normality result of Liu–Li–Pang [4] concerning shared values between two families. Let $\mathcal F$ and $\mathcal G$ be two families of meromorphic functions on D whose zeros are multiple. Suppose that $\mathcal G$ is normal on D, and no sequence contained in $\mathcal G$ $\chi$-converges locally uniformly to $\infty$ or a function g satisfying $g'\equiv 1$. If for every $f\in \mathcal F$, there exists a function $g\in \mathcal G$ such that f and g share 0 and $\infty$ while $f'$ and $g'$ share 1, then $\mathcal F$ is also normal on D.