Statistical limit superior and Statistical limit inferior in non-Archimedean L -fuzzy normed spaces

Abstract

The purpose of this article is to study the notion of statistical limit superior(SLS) and statistical limit inferior(SLI) in non-Archimedean(NA) $\mathfrak{L}$ -fuzzy normed spaces( $\mathfrak{L}$ -FNS). The concept of SLS and SLI is examined and extended to SLS and SLI in NA $\mathfrak{L}$ -FNS. Moreover, the analogue of some results between SLS and SLI over NA $\mathfrak{L}$ -FNS have been discussed. And also, it is proved that a bounded sequence is statistically convergent over NA $\mathfrak{L}$ -FNS. Throughout this article, $\mathcal{K}$ denotes a complete, non-trivially valued, non-Archimedean fields(NAF).