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International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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International Journal of Neutrosophic Science

Volume 26 , Issue 4 , PP: 204-218, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions

Isra Al-Shbeil 1 * , Wael Mahmoud Mohammad Salameh 2 , Jianhua Gong 3 , Ajmal Khan 4 , Shahid Khan 5

  • 1 Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan - (i.shbeil@ju.edu.jo)
  • 2 Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates - (wael.salameh@adu.ac.ae)
  • 3 Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates - (j.gong@uaeu.ac.ae)
  • 4 Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates - (ajmalkhan@aust.edu.pk)
  • 5 Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan - (drshahidmaths761@aust.edu.pk)

    • Doi: https://doi.org/10.54216/IJNS.260419

    Received: February 05, 2025 Revised: May 10, 2025 Accepted: June 09, 2025
    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 inequalities 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 sharpness and applicability of the results.

    Keywords :

    Neutrosophic analysis , Analytic functions , Univalent functions , Bi-univalent functions , Coefficient bounds , v-fold symmetric functions

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    Cite This Article As :
    Al-Shbeil, Isra. , Mahmoud, Wael. , Gong, Jianhua. , Khan, Ajmal. , Khan, Shahid. Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 204-218. DOI: https://doi.org/10.54216/IJNS.260419
    Al-Shbeil, I. Mahmoud, W. Gong, J. Khan, A. Khan, S. (2025). Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions. International Journal of Neutrosophic Science, (), 204-218. DOI: https://doi.org/10.54216/IJNS.260419
    Al-Shbeil, Isra. Mahmoud, Wael. Gong, Jianhua. Khan, Ajmal. Khan, Shahid. Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions. International Journal of Neutrosophic Science , no. (2025): 204-218. DOI: https://doi.org/10.54216/IJNS.260419
    Al-Shbeil, I. , Mahmoud, W. , Gong, J. , Khan, A. , Khan, S. (2025) . Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions. International Journal of Neutrosophic Science , () , 204-218 . DOI: https://doi.org/10.54216/IJNS.260419
    Al-Shbeil I. , Mahmoud W. , Gong J. , Khan A. , Khan S. [2025]. Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions. International Journal of Neutrosophic Science. (): 204-218. DOI: https://doi.org/10.54216/IJNS.260419
    Al-Shbeil, I. Mahmoud, W. Gong, J. Khan, A. Khan, S. "Coefficient Bounds for Generalized n-Fold Symmetric Neutrosophic Bi-univalent Functions," International Journal of Neutrosophic Science, vol. , no. , pp. 204-218, 2025. DOI: https://doi.org/10.54216/IJNS.260419

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