Statistical Convergence in $L$-Fuzzy Metric Spaces

Abstract

Statistical convergence, defined in terms of the natural density of positive integers, has been studied in many different spaces, such as intuitionistic fuzzy metric spaces, partial metric spaces, and $L$-fuzzy normed spaces. The main goal of this study is to define statistical convergence in $L$-fuzzy metric spaces ($L$-FMSs), one of the essential tools for modeling uncertainty in everyday life. Furthermore, this paper introduces the concept of statistical Cauchy sequences and investigates its relation with statistical convergence. Then, it defines statistically complete $L$-FMSs and analyzes some of their basic properties. Finally, the paper inquires the need for further research.

Keywords

• Statistical convergence
• statistical Cauchy sequences
• $L$-fuzzy metric spaces
• completeness

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