Recent Developments regarding Lacunary ∆-Statistical Convergence in Neutrosophic n-Normed Linear Spaces - J. Maduraiveeran; S. Satheesh Kanna; B. Silamparasan; J. Johnsy (Scientific Inquiry and Review, 2022)
The current paper's goal is to introduce lacunary ∆-statistically convergent and lacunary ∆-statistically Cauchy sequences in neutrosophic n-normed linear spaces, examine them and come to some significant conclusions about them. Also, we prove several useful results for these notions. We demonstrate how sequences in this space have some characteristics with 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 lacunary sequences that are ∆-statistically convergent and Cauchy. We demonstrate some inclusion results between the set of ∆-statistically convergent and lacunary ∆-statistically convergent sequences in neutrosophic n-normed linear spaces by generalizing the concepts for complex number sequences.