International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 249-252

A class of bounded starlike functions

Herb Silverman

Department of Mathematics, University of Charleston, Charleston 29424, SC, USA

Received 8 April 1993

Copyright © 1994 Herb Silverman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.