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.