(untitled) (Communications in Mathematical Research, 2019)
Let k be a positive integer and F be a family of meromorphic functions in a domain D such that for each fF, all poles of f are of multiplicity at least 2, and all zeros of f are of multiplicity at least k+1. Let a and b be two distinct finite complex numbers. If for each fF, all zeros of f^(k)-a are of multiplicity at least 2, and for each pair of functions f, gF, f^(k) and g^(k) share b in D, then F is normal in D.