A Certain Subclass of Meromorphically Convex Functions with Negative Coefficients

Abstract

In this paper we obtain coefficient inequalities, and distortion and closure theorems, for the class Λk(α, β, A, B) of meromorphically convex functions with negative coefficients, which we introduce here. We also obtain the class-preserving integral operator of the form:F(z)=c∫10ucf(uz)du (c>0)for the class Λk(α, β, A, B). Conversely, when the image function F(z)∈ Λk(α, β, A, B), we find the radius of convexity of the original function f(z). Several interesting results involving the modified Hadamard product of functions belonging to the class Λk(α, β, A, B) are also derived.