Coefficient estimates for some classes of functions associated with \(q\)-function theory

Abstract

In this paper, for every $q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach type problem for the class of $q$-convex functions of order $\alpha ,0\le \alpha <1$. In addition, we discuss the Fekete-szegö 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 $\alpha ,0\le \alpha <1$.

12 pages