# On the coefficient of The $n^{th}$ Cesaro mean of order $\alpha$ of bi-univalent functions

## TL;DR

This paper introduces a new subclass of bi-univalent functions in the unit disk and provides coefficient estimates for the second and third coefficients, advancing the understanding of their geometric properties.

## Contribution

It defines a novel subclass of bi-univalent functions and derives new bounds for their initial coefficients, extending existing coefficient estimate theories.

## Key findings

- Derived bounds for |a_2| and |a_3| coefficients
- Introduced a new subclass of bi-univalent functions
- Provided preliminary results related to the subclass

## Abstract

The purpose of the present paper is to introduce a new subclasses of the function class of bi-univalent functions defined in the open unit disc. Furthermore, we obtain estimates on the coefficients $|a_{2}|$ and $|a_{3}|$ for functions of this class. Some results related to this work will be briefly indicated.