Coefficient inequalities for univalent starlike functions

Let A be the class of analytic functions in the unit disk D 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 (z/f(z))μ = 1 + b1z + b2z2 +... to be starlike in D 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 D and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open. © 2013 Versita Warsaw and Springer-Verlag Wien.