Faber polynomial coefficient estimates for analytic bi-close-to-convex functions (Q2438555)

An analytic function \(f\) defined on the open unit disk \(\mathbb{D}\) is close-to-convex of order \(\alpha\), \(0\leq \alpha<1\), if there is a starlike function \(g\) such that \(\text{Re}(zf'(z)/g(z))>\alpha\). If both \(f\) and its inverse function \(f^{-1}\) extended to \(\mathbb{D}\) are close-to-convex of order \(\alpha\), then it is called a bi-close-to-convex function. For bi-close-to-convex functions of the form \(f(z)=z+a_nz^n+\cdots\), the authors obtain a bound for \(|a_n|\).