The Fekete-Szego Coefficient Inequality For a New Class of m-Fold Symmetric Bi-Univalent Functions Satisfying Subordination Condition

TL;DR

This paper introduces a new subclass of m-fold symmetric bi-univalent functions satisfying subordination, derives Fekete-Szeg"o inequalities, and estimates coefficients, expanding understanding of these functions and their properties.

Contribution

It presents a novel subclass of bi-univalent functions with m-fold symmetry satisfying subordination, along with new coefficient estimates and inequalities.

Findings

Derived Fekete-Szeg"o inequalities for the new class

Established coefficient bounds for the subclass

Connected results to existing function classes

Abstract

In this paper, we investigate a new subclass of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-Szeg\"o inequalities for this class. Also, we establish estimates for the coefficients for this subclas and several related classes are also considered and connections to earlier known results are made.