On Hankel Determinant H₂ (3) H 2 ( 3 ) for Univalent Functions

In this paper we consider the Hankel determinant H₂(3) = a₃a₅ - a₄² defined for the coefficients of a function f which belongs to the class S of univalent functions or to its subclasses: S^* of starlike functions, K of convex functions and R of functions whose derivative has a positive real part. Bounds of |H₂(3)| for these classes are found; the bound for R is sharp. Moreover, the sharp results for starlike functions and convex functions for which a₂=0 are obtained. It is also proved that max \|H₂(3)|: f∈ S\ is greater than 1.