Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions of Complex Order Associated with the Hohlov Operator

TL;DR

This paper introduces new subclasses of bi-univalent functions related to the Hohlov operator, providing estimates for initial MacLaurin coefficients and exploring their properties in the open unit disk.

Contribution

It defines novel subclasses of bi-univalent functions associated with the Hohlov operator and derives coefficient estimates for these classes.

Findings

Derived bounds for |a_2| and |a_3| coefficients.

Established properties of the new subclasses.

Connected results to existing function classes.

Abstract

In this paper we introduce and investigate two new subclasses of the function class $\Sigma$ of bi-univalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-MacLaurin coefficients $|a_2|$ and $|a_3|$ for functions in these new subclasses. Several known or new consequences of these results are also pointed out.