Some estimation about Tayler-Maclaurin coefficients of generalized subclasses of bi-univalent functions

TL;DR

This paper introduces new subclasses of bi-univalent functions, derives bounds for their Tayler-Maclaurin coefficients, and connects these findings to existing results in the field.

Contribution

It presents novel subclasses of bi-univalent functions and provides bounds for their Tayler-Maclaurin coefficients, extending previous research.

Findings

Bounds for second and third Tayler-Maclaurin coefficients established

Connections to and improvements on previous results

New subclasses of bi-univalent functions introduced

Abstract

Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of functions belonging to this subclasses were investigated. Furthermore, some improvement and connections to some of the previous known results are also pointed out.