Coefficient estimates for some families of bi-bazilevic functions of the ma-minda defined by convolution

TL;DR

This paper derives estimates for the Taylor-Maclaurin coefficients of bi-univalent Bazilevič functions of a certain order using convolution, contributing to the understanding of their coefficient bounds.

Contribution

It provides new coefficient estimates for bi-univalent Bazilevič functions of order γ using Hadamard product techniques.

Findings

Bounds on |a_2| and |a_3| coefficients for specific function classes.

Several known and new consequences derived from the estimates.

Enhanced understanding of bi-univalent Bazilevič functions' coefficient behavior.

Abstract

Making use of the Hadamard product(or convolution), we find some estimates on the Taylor-Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ for functions belong to bi univalent functions of the Bazilevi$\check{c}$ type of order $\gamma$. Several (known or new) consequences of the results are also pointed out.