Quasinormality of order 1 for families of meromorphic functions

Abstract

Let \mathscr{F} be a family of functions meromorphic on the plane domain D, all of whose zeros are multiple. Suppose that f^(k)(z)≠1 for all f∈\mathscr{F} and z∈D. Then if \mathscr{F} is quasinormal on D, it is quasinormal of order 1 there.