The fekete-szegö problem for close-to-convex functions with respect to the koebe function

An analytic function f in the unit disk D :={z ∈ ℂ : |z| < 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/2(1−z), z ∈ D if there exists δ∈(-π/2,π/2) such that Re{eiδ2(1−z)f′(z)} > 0, ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied.