Subclasses of meromorphically multivalent functions defined by a differential operator

Abstract

In this paper we introduce and study two new subclasses Σ λ μ m p ( α , β ) and Σ λ μ m p + ( α , β ) of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation and distortion theorems are obtained. We also extend the familiar concept of ( n , δ ) -neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.