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Upper bounds of the third hankel determinant for bi-univalent functions in crescent-shaped domains
(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Shakir, Qasim Ali; Tayyah, Adel Salim; Breaz, Daniel; Cotîrlă, Luminita-Ioana; Rapeanu, Eleonora; Sakar, Fethiye Müge
This paper investigates the third Hankel determinant, denoted (Formula presented.), for functions within the subclass (Formula presented.) of bi-univalent functions associated with crescent-shaped regions (Formula presented.). The primary aim of this study is to establish upper bounds for (Formula presented.). By analyzing functions within this specific geometric context, we derive precise constraints on the determinant, thereby enhancing our understanding of its behavior. Our results and examples provide valuable insights into the properties of bi-univalent functions in crescent-shaped domains and contribute to the broader theory of analytic functions. © 2024 by the authors.