On coefficient estimates for a certain class of starlike functions

Abstract

The purpose of this paper is to consider coefficient estimates in a class of functions S∗(q) consisting of analytic functions f normalized by f(0) = f′(0) − 1 = 0 in the open unit disk $\mathbb{U}$ which satisfies the subordination condition that$$zf'(z)/f(z)\prec q(z), z\in \mathbb{U},$$where $q(z)=\sqrt{1+z^2}+z$.