Some Normal Criteria about Shared Values with Their Multiplicity Zeros

Abstract

Let $ℱ$ be a family of meromorphic functions in the domain $D$, all of whose zeros are multiple. Let $\mathrm{n}(n\ge 2)$ be an integer and let $a$, $b$ be two nonzero finite complex numbers. If $f+a{(f\text{'})}^n$ and $g+a{(g\text{'})}^n$ share $b$ in $D$ for every pair of functions $f,g\in ℱ$, then $ℱ$ is normal in $D$.