aspg-21-2899-1791468676 20261008141116 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 4 Tariq Al-Hawary Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816. Jordan. Jadara University Research Center, Jadara University, Jordan. Ala Amourah Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 3111, Oman. Jadara University Research Center, Jadara University, Jordan. Jamal Salah College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman. Feras Yousef Department of Mathematics, The University of Jordan, Amman 11942, Jordan. School of Engineering, Math & Technology, Navajo Technical University, Crownpoint, NM 87313, USA. Jadara University R The aim of this article is to establish two new and qualitative subfamilies F(ε, κ, ℵ) and G(ε, κ, ℵ) of biunivalent functions. For functions in these subfamilies, we determine the first two Maclaurin coefficient estimations |C2| and |C3|, and address the Fekete–Szeg¨o problem. Additionally, we mention some corollaries related to the main results. 2024 315 323 2899 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240422 https://www.americaspg.com/journal/21/article/2899 https://www.americaspg.com/storage/11719105189.pdf