On Certain Classes of Multivalent Functions Involving a Generalized Differential Operator Defined by a Convolution

Abstract

Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed. Furthermore, we generalize the integral operator  studied by Frasin [11] and investigate sufficient conditions for the operator to be valentlystarlike, valently close-to-convex and uniformly valent close-to-convex.