aspg-21-3720-1791465333 20261008131533 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 2 M. Abu Saleem Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan Khalid Shebrawi Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan Tasnim Alkharabsheh Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan It is shown that if A, B,X, and Y are operators acting on a finite dimensional Hilbert space, then. ωu (AXB∗ ± BYA∗) ≤ 2 ∥A∥ ∥B∥ ωu ([0 X, Y 0]) where ωu (T ), ∥T ∥, are, respectively, the U-numerical radius, the spectral norm, of an operator T . 2025 279 291 3720 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260221 https://www.americaspg.com/journal/21/article/3720 https://www.americaspg.com/storage/81743019446.pdf