New subclasses of univalent functions on the unit disc in \(\mathbb{C}\)

In this paper we consider a differential operator \(\mathcal{G}_k\) defined on the family of holomorphic normalized functions \(\mathcal{H}_0(\mathbb{U})\) that can be used in the construction of new subclasses of univalent functions on the unit disc \(\mathbb{U}\). These new subclasses are closely related to the families of convex, respectively starlike functions on \(\mathbb{U}\). We study general results related to these new subclasses, such as growth and distortion theorems, coefficients estimates and duality results. We also present examples of functions that belongs to the subclasses defined.