On the second Hankel determinant of certain subclass of bi-univalent functions

In this paper, we define subclass D Sigma(delta,beta,alpha,t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {D}}_{\Sigma }(\delta ,\beta ,\alpha ,t)$$\end{document} of the function class Sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} of bi-univalent functions defined in the open unit disk in the complex plane. Using Chebyshev polynomials, we have investigated the upper bound for the second Hankel determinant for this function class.