In this paper, for every q∈(0,1), we obtain the Herglotz representation
theorem and discuss the Bieberbach type problem for the class of q-convex
functions of order α,0≤α<1. In addition, we discuss the
Fekete-szeg\"o problem and the Hankel determinant problem for the class of
q-starlike functions, leading to couple of conjectures for the class of
q-starlike functions of order α,0≤α<1.Comment: 12 page