New Subclasses of Analytic and Bi-Univalent Functions Endowed with Coefficient Estimate Problems

TL;DR

This paper introduces new subclasses of analytic and bi-univalent functions in the unit disk, providing coefficient estimates and connecting to prior results, thereby generalizing and enhancing existing theories.

Contribution

It proposes two new subclasses of bi-univalent functions and derives coefficient bounds, extending previous research in the field.

Findings

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

Connected new subclasses to existing function classes.

Generalized and improved upon earlier coefficient bounds.

Abstract

Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk U. For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor-Maclaurin coefficients |a_2| and |a_3|. Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of several earlier authors.