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)+zf″(z))>α, α<1. We find extreme points and then determine sharp lower bounds on Ref′(z) and Re(f(z)/z). Sharp results for the sequence of partial sums are also found.

Keywords

• univalent
• starlike.