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

For 0 < p < 1, let S_p 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 S_p (a) denote subclass of S_p consisting of those functions in S_p whose residue at the pole in equal to a. In this paper, we determine, for values of the residue a in a certain disk Δ_p, the greatest possible outer area over all functions in the class S_p (a). We also determine additional information concerning extremal function if the reside a dose not lie in Δ_p.