Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

Abstract

In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant $|a_2{a}_4-a_3^2|$ for functions belonging to the subclasses $S(\alpha ,\beta )$, $K(\alpha ,\beta )$, $S_s^{\ast }(\alpha ,\beta )$, and $K_s(\alpha ,\beta )$ of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.