This paper examines the set of
extreme points of the convex hull of families of analytic functions defined through
subordination. The set of extreme points is determined for the class of functions each
of which is subordinate to some starlike, univalent mapping of the open unit disk.
This set is also determined for the family defined by subordination to some
convex mapping, and a partial determination is obtained for subordination to
some close-to-convex mapping. This information is used to solve extremal
problems over such families. Results are also presented about the extreme
points for the functions which are subordinate to a given analytic function F.
For example, if f(z) = F(xz) and |x| = 1 then f is an extreme point. If
F ∈ Hp,1 < p < ∞, and ϕ is an inner function with ϕ(0) = 0, then F(ϕ) is an
extreme point.
