Upper bound for the second Hankel determinant of certain subclass of analytic and bi-univalent functions

TL;DR

This paper establishes an upper bound for the second Hankel determinant within a specific subclass of analytic and bi-univalent functions, utilizing Chebyshev polynomials to derive the estimate.

Contribution

It introduces a new upper bound estimate for the second Hankel determinant for a certain subclass of bi-univalent functions using Chebyshev polynomials.

Findings

Derived an explicit upper bound for the second Hankel determinant.

Applied Chebyshev polynomials to analyze the function class.

Provides theoretical bounds relevant to geometric function theory.

Abstract

In this paper, we consider a general subclass of analytic and bi-univalent functions in the open unit disk in the complex plane. Making use of the Chebyshev polynomials, we obtain upper bound estimate for the second Hankel determinant for this function class.