Arithmetic statistically convergent on neutrosophic normed spaces

Abstract

This work is concerned with several important different types of convergence that will be described on neutrosophic normed spaces. In the study, arithmetic convergence was combined with different types of statistical convergence and then integrated into the structure of neutrophic spaces established through the membership function. For this purpose, in the neutrophic normed space, firstly, some important definitions that can be established with lacunary sequence, ideal structures and arithmetic convergent, arithmetic statistical convergence concepts are given, and then some relationships between convergent sequences in this sense are examined. Then, new convergence definitions were established by evaluating lambda sequences together with arithmetic convergence and statistical convergence with the help of Neutrophic normed space structure properties. Finally, with the help of the definitions of degree of convergence, the inclusion relationship between the two set is given.