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

Abstract

. We discuss the sharpness of the bound of the Fekete–Szegö functional for close-to-convex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete–Szegö functional | a 3 − λa 22 | (0 6 λ 6 1) as well as the corresponding Hankel determinant for the Taylor–Maclaurin coefficients { a n } n ∈ Nr { 1 } of normalized univalent functions in the open unit disk D , N being the set of positive integers.