Fekete-Szeg\"o problem for certain classes of Ma-Minda bi-univalent functions

TL;DR

This paper investigates Fekete-Szeg"o inequalities for specific classes of bi-univalent functions defined via subordination, providing improved bounds on the third coefficient and discussing applications.

Contribution

It introduces new bounds for the third coefficient of bi-univalent functions within certain classes, enhancing existing results and exploring applications.

Findings

Improved bounds on the third coefficient for bi-univalent functions.

New inequalities related to Fekete-Szeg"o problem.

Applications demonstrating the usefulness of the bounds.

Abstract

In the present work, we propose to investigate the Fekete-Szeg\"o inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.