Some remarks on summability on neutrosophic normed spaces

Archana Sharma¹, Sajid Murtaza², Vijay Kumar^3,*

^1,2,3 Department of Mathematics, Chandigarh University, Gharuan Mohali (Punjab), India

Emails: dr.archanasharma1022@gmail.com; sajidsulimani8@gmail.com; kaushikvjy@gmail.com

Abstract

In the present paper, we use the difference operator  and  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.

Keywords: Neutrosophic normed spaces; lacunary convergence; and I-convergence.