Bounds for the Second Hankel Determinant of Certain Univalent Functions

TL;DR

This paper derives bounds for the second Hankel determinant of various classes of univalent functions, including strongly starlike and lemniscate starlike functions, using subordination techniques.

Contribution

It provides new estimates for the second Hankel determinant for several classes of univalent functions, expanding understanding of their geometric properties.

Findings

Bounds for the second Hankel determinant of certain univalent functions are established.

Explicit estimates are obtained for strongly starlike, parabolic starlike, and lemniscate starlike functions.

The results extend previous work by applying subordination conditions to derive these bounds.

Abstract

The estimates for the second Hankel determinant a_2a_4-a_3^2 of analytic function f(z)=z+a_2 z^2+a_3 z^3+...b for which either zf'(z)/f(z) or 1+zf"(z)/f'(z) is subordinate to certain analytic function are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike, lemniscate starlike functions are obtained.