Second Hankel determinant for a certain subclass of bi-close to convex functions defined by Kaplan

TL;DR

This paper investigates the second Hankel determinant bounds for specific subclasses of bi-close-to-convex functions, providing improved estimates over previous results in the field.

Contribution

It introduces new upper bounds for the second Hankel determinant for strongly bi-close-to-convex functions of order α and bi-close-to-convex functions of order β, enhancing existing results.

Findings

Established upper bounds for the second Hankel determinant

Improved upon previous estimates for bi-convex functions

Extended results to subclasses of bi-close-to-convex functions

Abstract

In this paper, we consider the class of strongly bi-close-to-convex functions of order $\alpha$ and bi-close-to-convex functions of order $\beta$. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.