Coefficient bounds for new subclasses of bi-univalent functions

TL;DR

This paper introduces two new subclasses of bi-univalent functions in the unit disk and derives upper bounds for their second and third coefficients, advancing the understanding of their coefficient estimates.

Contribution

The paper defines novel subclasses of bi-univalent functions and establishes new coefficient bounds for these classes, expanding the theoretical framework in geometric function theory.

Findings

Derived upper bounds for second coefficients

Derived upper bounds for third coefficients

Introduced new subclasses of bi-univalent functions

Abstract

In the present investigation, we consider two new subclasses N_{{\Sigma}}^{{\mu}}({\alpha},{\lambda}) and N_{{\Sigma}}^{{\mu}}({\beta},{\lambda}) of bi-univalent functions defined in the open unit disk U={z:|z|<1}. Besides, we find upper bounds for the second and third coefficients for functions in these new subclasses.