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- Title
On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions.
- Authors
Shakir, Qasim Ali; Atshan, Waggas Galib
- Abstract
This study presents a subclass S (β) of bi-univalent functions within the open unit disk region D . The objective of this class is to determine the bounds of the Hankel determinant of order 3, ( Ⱨ 3 (1) ). In this study, new constraints for the estimates of the third Hankel determinant for the class S (β) are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as S (β) and impose constraints on the coefficients │ a n │ . Our investigation provides the upper bounds for the bi-univalent functions in this newly developed subclass, specifically for n = 2, 3, 4, and 5. We then derive the third Hankel determinant for this particular class, which reveals several intriguing scenarios. These findings contribute to the broader understanding of bi-univalent functions and their potential applications in diverse mathematical contexts. Notably, the results obtained may serve as a foundation for future investigations into the properties and applications of bi-univalent functions and their subclasses.
- Subjects
UNIVALENT functions; GEOMETRIC function theory; HANKEL functions; GEOMETRIC analysis; ANALYTIC functions; MATHEMATICS
- Publication
Symmetry (20738994), 2024, Vol 16, Issue 2, p239
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym16020239