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 Upper bound of second Hankel determinant for a subclass of bi-univalent functions of complex order Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 783-797 https://doi.org/10.4134/CKMS.c180212Published online July 31, 2019 Nizami Mustafa Kafkas University Abstract : 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 Full-Text :