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
oleh: Timilehin Gideon Shaba, Serkan Araci, Babatunde Olufemi Adebesin, Fairouz Tchier, Saira Zainab, Bilal Khan
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2023-06-01 |
Deskripsi
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.