A Class of Meromorphic Multivalent Functions with Negative Coefficients Defined by a Ruscheweyh-Type Operator

We introduce and systematically study a new class kλ,p(α,β) of meromorphic p-valent functions defined by means of the Ruscheweyh-type operator D*λ,p, where p∈N, λ>−p, 0≤α<1, and β>0. Membership in this class is characterized through coefficient estimates. Also investigated are growth, distortion, stability under convex combinations, radii of starlikeness and convexity of order ρ(0≤ρ<1), convolution, the action of an integral operator of Bernardi–Libera–Livingston type, and neighborhoods.