Coefficient Bounds for a Subclass of Bi-Univalent Functions

Alifira Meliana Rachman (Department of Mathematics, Faculty of Science, Technology, and Mathematics, Brawijaya University, Malang)
Marjono Marjono (Department of Mathematics, Faculty of Science, Technology, and Mathematics, Brawijaya University, Malang)
Sa’adatul Fitri (Department of Mathematics, Faculty of Science, Technology, and Mathematics, Brawijaya University, Malang)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

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 Carathodory 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.