A Certain Fractional Derivative Operator and Its Applications to a New Class of Analytic and Multivalent Functions with Negative Coefficients, II

Recently, the authors made use of a certain operator of fractional derivatives in order to introduce (and initiate a systematic study of) a novel subclass Tp(α, β, λ) of analytic and p-valent functions with negative coefficients. In this sequel to the aforementioned work, they prove a number of closure and inclusion theorems and determine the radii of p-valently close-to-convexity, starlikeness, and convexity for the class Tp(α, β, λ). They also obtain a class-preserving integral operator of the form: F(z) = (Jγ,pƒ)(z) ≔ γ+pzγ ∫z0tγ−1 ƒ(t) dt (γ > −p) for the class studied here.