Second Hankel determinant for close-to-convex functions

So far, the sharp bound of the expression | a 2 a 4 − a 3 2 | for the class C of close-to-convex functions has remained unknown. In this paper, we obtain the estimation of this expression, called the second Hankel determinant, for C 0, i. e. the subset of C consisting of functions f that satisfy in the unit disk the inequality Re (z f ′ (z) / g (z) ) > 0 with a starlike function g. Moreover, some remarks on the second Hankel determinant for the class S of univalent functions are made. It is proven that max ⁡ | a 2 a 4 − a 3 2 |: f ∈ S is greater than 1.