Certain classes of analytic functions concerned with uniformly starlike and convex functions

Abstract

Applying the coefficient inequalities of functions f( z) belonging to the subclasses MD ( α , β ) and ND ( α , β ) of certain analytic functions in the open unit disk U , two subclasses MD ∗ ( α , β ) and ND ∗ ( α , β ) are introduced. The object of the present paper is to derive some convolution properties of functions f( z) in the classes MD ∗ ( α , β ) and ND ∗ ( α , β ) .