Linear spaces and linear-invariant families of locally univalent analytic functions

Let X be the set of functions f analytic in the unit disk D with derivatives f(z)0 in D, that satisfy the growth restriction f(z)/f(z)=0((1–|z|)^–1 (zD). The set X is equipped with a normed linear space structure. The topological structure of X and its relationship with linear-invariant families of locally univalent functions is investigated.This research was supported by the U. S. Army Research Office-Durham, Grant DA-ARO-D-31-124-G1151.