Certain class of meromorphically multivalent functions defined by a differential operator

Abstract

In this paper, we introduce the subclasses Tp(α, δ, A, B, n) and T∗p (α, δ, A, B, n) of meromorphic multivalent functions in the punctured unit disk U∗ = {z ∈ C : 0 < |z| < 1} by using a differential operator Dnδ,p f (z). We obtain coefficient estimates, distortion theorem, radius of convexity and closure theorems for the class T∗p (α, δ, A, B, n). The familiar concept of neighborhoods of analytic functions is also extended and applied to the functions considered here.