In this paper the classes of uniformly convex and uniformly starlike functions are presented as dual sets for certain function families (in the sense of convolution theory). The results are used to find some sharp sufficient ...
We study the integral operator Pλ[f](ζ) = ∫ ζ0 ζ(f′(t))λ dt, |ζ| > 1, acting on the class ∑ of functions meromorphic and univalent in the exterior of the unit disk. We refine the ranges of the parameter λ for which the ...