Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce and investigate a subclass \linebreak $\Im _{\Sigma }\left( \alpha ,\beta ,{\gamma }\right) $ of analytic and bi-univalent functions of complex order in the open unit disk $U$ in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

Keywords: analytic functions, univalent functions, bi-univalent functions, Hankel determinant

MSC numbers: Primary 30C45, 30C50; Secondary 30C80