Concave schlicht functions with bounded opening angle at infinity (Q1780375)

Let \(CO(A)\), \(A\in(1, 2)\) denote the class of functions \(f(z)= z+ a_2(f) z^2+\cdots\) that map the open unit disc \(D\) conformally onto a domain whose complement with respect to \(\mathbb{C}\) is convex and such that \(f(1)=\infty\) and the opening angle of \(f(D)\) at infinity is less than or equal to \(\pi A\). In this paper the authors generalized the earlier results, where the case \(A= 2\) is considered, and obtained the representation formulas for the functions \(f\) in \(CO(A)\) (Theorem: 2). They determined the domains of variability of \(a_2(f)\) and \(a_3(f)\), \(f\in CO(A)\) (Cor. 1 and 3) and also the Koebe domain of \(CO(A)\) (Theorem 3).