A note on the Fekete-Szegö problem for close-to-convex functions with respect to convex functions

We discuss the sharpness of the bound of the Fekete-Szego functional for close-to-convex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete-Szego functional |a3? ? a22| (0? ? ? 1) as well as the corresponding Hankel determinant for the Taylor-Maclaurin coefficients ann? N\1 of normalized univalent functions in the open unit disk D, N being the set of positive integers.