Fekete-Szeg\"o problem and Second Hankel Determinant for a class of bi-univalent functions

TL;DR

This paper studies a specific subclass of bi-univalent functions in the unit disk, deriving bounds for coefficients, Fekete-Szeg"o inequality, and second Hankel determinant, extending previous work with new bounds and special cases.

Contribution

It introduces new bounds for coefficients and inequalities for a subclass of bi-univalent functions, expanding the theoretical understanding of their properties.

Findings

Bounds for initial coefficients derived

Fekete-Szeg"o inequality established

Second Hankel determinant inequality obtained

Abstract

In this sequel to the recent work (see Azizi et al., 2015), we investigate a subclass of analytic and bi-univalent functions in the open unit disk. We obtain bounds for initial coefficients, the Fekete-Szeg\"o inequality and the second Hankel determinant inequality for functions belonging to this subclass. We also discuss some new and known special cases, which can be deduced from our results.