On a maximal outer area problem for a class of meromorphic univalent fuctions

Abstract

For 0 < p < 1, let Sp denote the class of functions f (z) which are meromorphic and univalent in the unit disk U, with the normalisations f (0) = 0, f′(0) = 1 and f (p) = ∞, and let Sp (a) denote subclass of Sp consisting of those functions in Sp whose residue at the pole in equal to a. In this paper, we determine, for values of the residue a in a certain disk Δp, the greatest possible outer area over all functions in the class Sp (a). We also determine additional information concerning extremal function if the reside a dose not lie in Δp.