+ B(z)zp'(z) + C(z)p(z) + D(z) Mz

Using this last result and condition (ii) together with (4.1-10) we deduce that

Instead of prescribing the constant N in Theorem 4.lb, in some cases we can use (ii) to determine an appropriate N = N(M, n, B, C, D) so that (4.1-8) implies I p(z) I < N. This can be accomplished by solving (ii) for N and by taking the supremum of the resulting function over U. If this supremum is finite, we have the following version of Theorem 4.1 b.