On A Certain Subclass of Analytic Functions Defined Via a Generalized Differential Operator

Abstract

In this paper we introduce and study several new subclasses of analytic and univalent functions in the open unit disk defined by means of a generalized differential operator. The operator generalizes numerous differential operators which have been widely used in geometric function theory. Using standard techniques involving subordination and Carath’eodory functions, we derive comprehensive coefficient estimates, the Fekete–Szegő inequality, bounds for the second Hankel determinant, inclusion relationships, neighborhood properties, Growth and Distortion properties. The results obtained in this work generalize and unify several earlier results in the literature.