CERTAIN SUBCLASSES OF MEROMORPHICALLY P-VALENT FUNCTIONS WITH POSITVE OR NEGATIVE COEFICIENTS USING DIFFERENTIAL OPERATOR

Abstract

In this paper, we have introduced two subclasses AR(λ,k,p,ζ,δ) and AC(λ,k,p,ζ,δ) of meromorphically p-valent functions with positive and negative coefficients, defined by differential operator in the punctured unit disk U^*= {z:z∈ C; 0<|z|<1}=U\{0} and obtain some sharp results including coefficient inequality, distortion theorem, radii of starlikeness and convexity, closure theorems of these subclasses of meromorphically p-valent functions. We also derive some interesting results for the Hadamard products of functions belonging to the classes AR(λ,k,p,ζ,δ) and AC(λ,k,p,ζ,δ).