Applications of extreme point theory to classes of multivalent functions

Abstract

Extreme points of the closed convex hulls of several classes of multivalent functions are determined. These are then used to determine the precise bounds on the coefficients of a function majorized by or subordinate to a function in any of the classes. L q {L^q} means are also discussed and subordination theorems are considered. The classes we consider are generalizations of the univalent starlike, convex and close-to-convex functions in addition to others.