International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1260 2020 2020 Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India Archana Sharma Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India Sajid Murtaza Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India Vijay Kumar In the present paper, we use the difference operator ∆m (Iλ )-summability to define some new summability concepts on neutrosophic normed spaces. We also introduce concepts of generalized limit point, and cluster point and obtain some relationships among these notions. Finally, we define generalized Cauchy sequences on these spaces and present a characterization of a new summability method that preserves linear operators on neutrosophic normed spaces. 2022 2022 68 81 10.54216/IJNS.190105 https://www.americaspg.com/articleinfo/21/show/1260