A class of bounded starlike functions

Abstract

We consider functions f ( z ) = z + … that are analytic in the unit disk and satisfy there the inequality Re( f ′ ( z ) + z f ″ ( z )) > α , α < 1. We find extreme points and then determine sharp lower bounds on Re f ′ ( z ) and Re( f ( z )/ z ). Sharp results for the sequence of partial sums are also found.