Application of three leaf domain on a subclass of bi-univalent functions - Shaba, Timilehin Gideon; Araci, Serkan; Adebesin, Babatunde Olufemi; Aracı, Serkan (Institute of Electrical and Electronics Engineers Inc., 2024)
In this manuscript, our inspiration stems from recent advancements in research and the widely recognized notion of coefficient estimates applicable to analytic and bi-univalent functions(BF) categories. Initially, we introduce fresh subcategories, denoted as \mathcal{T}{\mathcal{D}_\Sigma }, within the realm of analytic functions(AF) and BF. These subcategories are intricately linked with the concept of a three-leaf domain. Subsequently, we tackle the Fekete-Szegö problem within the scope of the \mathcal{T}{\mathcal{D}_\Sigma } class that pertains to a three-leaf domain. We concentrate on setting boundaries for the coefficients, as well as defining a maximum limit for the second Hankel determinant(HD). Notably, it should be emphasized that nearly all outcomes attain their utmost precision, accompanied by the presentation of their respective extreme functions. © 2024 IEEE.
Keywords: Biunivalent functions; Bounded turning functions; Fekete-Szegö inequality; hankel determinant; Three leaf domain