Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Suhila Elhaddad,Maslina Darus

doi:10.3390/math8030306

Abstract

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

Highlights

Geometric function theory research has provided analysis of a number of subclasses of A, as a class of normalised analytic function, using a range of approaches
Q-calculus has been widely applied in investigating a number of such subclasses within the open unit disk ∆. ∂q as a q-derivative operator was initially applied by Ismail et al [1] in studying a specific q-analogue within ∆ in the starlike function class
Such q-operators were approximated and their geometric properties examined by Mohammed and Darus [2] for several analytic function subclasses within compact disks

Summary

Introduction

Geometric function theory research has provided analysis of a number of subclasses of A, as a class of normalised analytic function, using a range of approaches. ∂q as a q-derivative operator was initially applied by Ismail et al [1] in studying a specific q-analogue within ∆ in the starlike function class. Such q-operators were approximated and their geometric properties examined by Mohammed and Darus [2] for several analytic function subclasses within compact disks. Σ represents the bi-univalent function class which Equation (1) defines. The aim of the present work is to introduce Sqδ (θ, η, ρ, ν; ψ) as a general subclass of Σ as a class of bi-univalent functions. Some useful work associated with inequalities and their properties can be read in [44,45,46,47]

A Set of Main Results

Applications of the Main Result

Conclusions