Upper bound of second Hankel determinant of subclass of bi-univalent functions defined by subordination

TL;DR

This paper introduces a new subclass of bi-univalent functions defined via subordination and establishes an upper bound for their second Hankel determinant, correcting previous miscalculations and extending existing results.

Contribution

It defines a new bi-univalent function subclass via subordination and provides a corrected, sharper upper bound for the second Hankel determinant within this class.

Findings

Established an upper bound for |H_2(2)| for the new subclass

Corrected previous miscalculations in related results

Extended the theoretical framework for bi-univalent functions

Abstract

In this paper, new class of bi-univalent functions are introduced. Upper bound of the second Hankel determinant $|H_2(2)|$ of subclass of bi-univalant functions class $\Sigma$, which defined by subordination, investigated. Furthermore, some results concluded as a special case of our main results and corrected some previous researchers results which investigated by miscalculation.