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 (α, β), K (α, β), S s (α, β), and K s (α, β) of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors. © 2014 Ming-Sheng Liu et al.