On the Normal Meromorphic Functions

Let F be a family of functions meromorphic in D such that all the zeros of f Є F are of multiplicity at least k (a positive integer), and let E be a set containing k + 4 points of the extended complex plane. If, for each function f Є F, there exists a constant M and such that (1−|z|^2)^k|f^(k)(z)|/(1+|f(z)|^k+1) ≤ M whenever z Є {f(z) Є E, z Є D}, then F is a uniformly normal family in D, that is, sup{(1 − |z|^2)f^#(z) : z Є D, f Є F} (infinity)