Coefficient inequalities for univalent starlike functions

Let A be the class of analytic functions in the unit disk with the normalization f (0) = f ′(0) − 1 = 0. In this paper the authors discuss necessary and sufficient coefficient conditions for f ∈ A of the form to be starlike in and more generally, starlike of some order β , 0 ≤ β < 1. Here µ is a suitable complex number so that the right hand side expression is analytic in and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open.