Second Hankel determinant for bi-starlike and bi-convex functions of order β

In the present investigation the authors obtain upper bounds for the second Hankel determinant H2(2) of the classes bi-starlike and bi-convex functions of order β  , represented by Sσ*(β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinant H2(2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.