Second Hankel Determinant of Bi-univalent Functions

Abstract

Let  be the class of functions which are analytic in the open unit disk and having the form . Denote  to be the class for all functions in  that are univalent in . Then, let  denote the class of bi-univalent functions in . In this paper, we obtain the second Hankel determinant for certain classes of analytic bi-univalent function which are defined by subordinations in the open unit disk . In particular, we determine the initial coefficients  and  and obtained the upper bound for the functional  of functions  in the classes of analytic bi-univalent function which are defined by subordinations in .