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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 249-252
doi:10.1155/S0161171294000360

A class of bounded starlike functions

Herb Silverman

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

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.