Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel <i>q</i>-Differential Operator Associated with <i>q</i>-Limaçon Domain

Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel <i>q</i>-Differential Operator Associated with <i>q</i>-Limaçon Domain

In this present paper, we define a new operator in conjugation with the basic (or <i>q</i>-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the <i>q</i>-derivative operator. Furthermore,...

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Bibliographic Details
Main Authors: Timilehin Gideon Shaba, Serkan Araci, Babatunde Olufemi Adebesin, Fairouz Tchier, Saira Zainab, Bilal Khan
Format: Article
Language:English
Published: MDPI AG 2023-06-01
Series:Fractal and Fractional
Subjects:
q-limaçon domain
Bi-univalent functions
Hankel determinant
starlike function
Fekete–Szegö inequality
Online Access:https://www.mdpi.com/2504-3110/7/7/506
Description
Summary:In this present paper, we define a new operator in conjugation with the basic (or <i>q</i>-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the <i>q</i>-derivative operator. Furthermore, we find the initial Taylor–Maclaurin coefficients for these newly defined function classes of analytic and bi-univalent functions. We also show that these bounds are sharp. The sharp second Hankel determinant is also given for this newly defined function class.
ISSN:2504-3110

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