Second Hankel determinant for a certain function class of bi-univalent functions associated with Salagean derivative operator

Abstract

In this work, we investigate the bounds on the fourth initial coefficient $|a_4|$ and the second Hankel determinant $|a_2a_4 - a^ 2_3|$ for a class of analytic and bi-univalent functions defined in the open unit disk. The class is connected with the Salagean differential operator and involves a linear combination of the classes of strongly bi-starlike functions and strongly bi-convex functions. It was also shown that the investigated class generalized many known classes by varying the parameters in the definition of the class.