Coefficient Bounds for a Subclass of Bi-Univalent Functions

Alifira Meliana Rachman, Marjono Marjono, Sa’adatul Fitri

Abstract


In this paper, we obtain explicit upper bounds for the initial seven coefficients and their inverses for a subclass of bi-univalent functions defined via subordination. Using coefficient estimates associated with the Carathéodory class and coefficient comparison techniques, expressions for the bounds of a2, a3, …, a7 are derived. Moreover, it is proved that the first seven inverse coefficients admit the same upper bounds as the corresponding coefficients of the original function. These findings generalize several existing results concerning lower-order coefficients and provide a framework for further investigations of higher-order coefficient and Hankel determinant problems in the theory of bi-univalent functions.


Keywords


Analytic Functions; Bi-univalent Functions; Carathéodory Functions; Initial Coefficient Estimates; Inverse Coefficient.

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DOI: https://doi.org/10.18860/cauchy.v11i2.43761

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