Fekete-Szegö problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter

Given α ∈ [0, 1], let hα(z):= z/(1 - αz), z ∈ D:= {z ∈ D: |z| < 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{eiδzf′(z)/hα(z)} > 0, z ∈ D. For the class ℓ (hα) of all close-to-convex functions with respect to hα, the Fekete-Szegö problem is studied.