Normality criteria of meromorphic functions with multiple zeros

Take positive integers n , k ⩾ 2 . Let F be a family of meromorphic functions in a domain D ⊂ C such that each f ∈ F has only zeros of multiplicity at least k. If, for each pair ( f , g ) in F , f ( f ( k ) ) n and g ( g ( k ) ) n share a non-zero complex number a ignoring multiplicity, then F is normal in D.