Fekete-Szeg\"o inequality of bi-starlike and bi-convex functions of order $b$ associated with symmetric $q$-derivative in conic domains

TL;DR

This paper introduces new subclasses of bi-univalent functions defined via symmetric q-differential operators in conic domains, and establishes initial bounds for the Fekete-Szeg"o inequality for these classes.

Contribution

It defines novel bi-univalent function subclasses related to conic domains using symmetric q-differential operators and derives initial Fekete-Szeg"o bounds for them.

Findings

Established initial bounds for Fekete-Szeg"o inequality

Defined new subclasses of bi-univalent functions in conic domains

Utilized symmetric q-differential operators in analysis

Abstract

In this paper, two new subclasses of bi-univalent functions related to conic domains are defined by making use of symmetric $q$-differential operator. The initial bounds for Fekete-Szeg\"o inequality for the functions $f$ in these classes are estimated.