aspg-21-3115-1791475461 20261008160421 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 2 Alaa Adnan Auad Department of Mathematics, College of Education for pure science, University of Anbar, Iraq Mohammed A. Hilal Middle Technical University, Technical Institute of Baquba, Diyala, Iraq A neutrosophic is a strong framework to characterize novel mathematical structures. This framework is more suitable and flexible set side by side to fuzzy sets and intuitionistic fuzzy sets. In this work, we focus on some famous mathematical spaces like Ls,p (u)when we work on displaying a feature the immediate and contrary theorems of unrestrained functions in the spaceLs,p (u)are considered. Also, some characteristics of modification symmetric and modulus of neutrosophic smoothness have been discussed. Moreover, the identical among approximate tools such as the neutrosophic K-functional and neutrosophic modulus of softness. 2025 57 63 3115 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250206 https://www.americaspg.com/journal/21/article/3115 https://www.americaspg.com/storage/41723891424.pdf