Recent Developments regarding Lacunary ∆-Statistical Convergence in Neutrosophic n-Normed Linear Spaces

Abstract

The current paper's goal is to introduce lacunary ∆-statistically convergent andlacunary ∆-statistically Cauchy sequences in neutrosophic n-normed linear spaces, examinethem and come to some significant conclusions about them. Also, we prove several usefulresults for these notions. We demonstrate how sequences in this space have some characteristicswith lacunary ∆-statistical convergence of real sequences. In contrast to other related works, we define the concept of convergence of a sequence in neutrosophic n-normed linear spaces in this study. We have also established the results using a new methodology. Additionally, we provide some novel descriptions for lacunarysequences that are ∆-statistically convergent and Cauchy. We demonstrate some inclusionresults between the set of ∆-statistically convergent and lacunary ∆-statistically convergentsequences in neutrosophic n-normed linear spaces by generalizing the concepts for complex number sequences.