International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3906 2020 2020 Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Faisal Faisal Ministry of Education, General Directorate of Education, Baghdad, Third Rusafa, Iraq Raad Falh Hasan College of Administration and Economics, Diyala University, Iraq Abed S.. A. Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi The concentration of linear operators is unpretentious to prove in measurable space   but there is few works in weighted space, here we will include characteristics of approximate of unrestrained functions in measured space by lined operators via direct and converse approximation theorems. In addition, the relationship between modulus of softness and K- functional where, we proven are together tools equivalence. 2025 2025 167 173 10.54216/IJNS.260416 https://www.americaspg.com/articleinfo/21/show/3906