Analytic functions of non-Bazilevič type and starlikeness (Q1599759)

Let \(\alpha=(\alpha_1, \alpha_2, \dots, \alpha_k)\), \(\alpha_j \in\mathbb{R}\), \(j=1\) to \(k\) and \(D_\alpha= 1+\alpha_1 z{d\over dx}+\alpha_2 z^k {d^k\over dz^k}\). The authors define in terms of the operator \(D_\alpha\) two classes of functions analytic in the unit disk and they answer some questions concerning starlikeness.