Faber polynomial coefficient estimation of subclass of bi-subordinate univalent functions

TL;DR

This paper introduces a new subclass of bi-univalent functions, estimates their Faber polynomial coefficients, and improves existing inequalities related to their Maclaurin expansion.

Contribution

It defines a comprehensive bi-univalent subclass and provides novel coefficient estimates and Fekete-Szeg"o inequalities using Faber polynomials.

Findings

Derived bounds for coefficients |a_n|

Established Fekete-Szeg"o inequalities

Improved previous results on bi-univalent functions

Abstract

In this paper, a comprehensive subclass of bi-univalent functions class are introduced and investigated. Using the Faber polynomials, estimation of the coefficients $|a_n|$ and certain Fekete-Szeg\"{o} inequality of Maclaurin expansion of functions in this subclass are concluded. Finally, some earlier results are pointed out and improved.