Second Hankel determinant for bi-starlike and bi-convex functions of order \b{eta}

TL;DR

This paper establishes upper bounds for the second Hankel determinant in the classes of bi-starlike and bi-convex functions of a given order, advancing the understanding of their geometric properties.

Contribution

It provides new upper bounds for the second Hankel determinant specifically for bi-starlike and bi-convex functions of order beta, which was not previously known.

Findings

Derived upper bounds for the second Hankel determinant

Applied bounds to bi-starlike functions of order beta

Applied bounds to bi-convex functions of order beta

Abstract

In the present investigation the authors obtain upper bounds for the second Hankel determinant of the classes bi-starlike and bi-convex functions of order beta.