Certain classes of analytic functions concerned with uniformly starlike and convex functions (Q884132)

Applying the coefficient inequalities of functions \(f(z)\) belonging to the subclasses \({\mathcal M}{\mathcal D}(\alpha,\beta)\) and \({\mathcal N}{\mathcal D}(\alpha,\beta)\) of certain analytic functions in the open unit disk \(\mathbb U\), two subclasses \({\mathcal M}{\mathcal D}^*(\alpha,\beta)\) and \({\mathcal N}{\mathcal D}^*(\alpha,\beta)\) are introduced. The object of the present paper is to derive some convolution properties of functions \(f(z)\) in the classes \({\mathcal M}{\mathcal D}^*(\alpha,\beta)\) and \({\mathcal N}{\mathcal D}^*(\alpha,\beta)\).