GENERALIZED CLASS OF UNIVALENT FUNCTIONS WITH TWO FIXED POINTS

Univalent functions of the form \[ f(z)= a_1z-\sum_{n=2}^\infty a_nz^n\] where $a_n \ge 0$, are dealt with. We examine the subclasses for which $(1 - \lambda)f(z_0)/z_0+\lambda f'(z_0) =1$ ($-1 <z_0 <1$). The coefficient inequali- ties and the extreme points of the classes that are starlike and convex of order o are determined. Many of the results of Silverman are obtained as particular cases.