Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic
Bi-univalent Functions
Isra Al-Shbeil1,∗, Wael Mahmoud Mohammad Salameh2, Jianhua Gong3,∗, Ajmal Khan4,
Shahid Khan4
1Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
2Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates
3Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab
Emirates
4Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500,
Pakistan
Emails: i.shbeil@ju.edu.jo; wael.salameh@adu.ac.ae;j.gong@uaeu.ac.ae; ajmalkhan@aust.edu.pk;
drshahidmaths761@aust.edu.pk
Abstract
In this paper, we introduce and investigate new generalized subclasses of neutrosophic n-fold symmetric bi-
univalent functions defined in the open unit disk U . These subclasses are characterized via four neutrosophic
multi-parameters κ, ρ, γ, and β, which provide a flexible framework to capture the truth, indeterminacy, and
falsity components inherent in geometric and analytic behaviors. Within this neutrosophic setting, we derive
upper bounds for the initial coefficients |dn+1| and |d2n+1|, and establish generalized Fekete–Szeg˝o inequal-
ities for the considered classes. The results obtained extend and unify several existing results in classical and
neutrosophic bi-univalent function theory. Examples and corollaries are presented to demonstrate the sharp-
ness and applicability of the results