Coefficient estimate of bi-Bazilevi\u{c} function of complex order based on quasi subordination involving Srivastava-Attiya operator

TL;DR

This paper introduces a new subclass of bi-univalent functions related to the Hurwitz-Lerch zeta function, providing coefficient estimates and exploring their properties within complex analysis.

Contribution

It defines a novel subclass of bi-univalent functions involving the Hurwitz-Lerch zeta function and derives coefficient bounds under quasi-subordination conditions.

Findings

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

Established properties of the new subclass.

Connected results to known function classes.

Abstract

In this paper, we introduce and investigate a new subclass of the function class $\Sigma$ of bi-univalent functions defined in the open unit disk, which are associated with the Hurwitz-Lerch zeta function, satisfying quasi-subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in this new subclass. Several (known or new) consequences of the results are also pointed out.