On mathcal{I}_{{theta}_{2}}-convergence in fuzzy normed spaces

Muhammed Recai Türkmen

doi:10.1186/s13660-020-02387-9

Muhammed Recai Türkmen

Open Access

https://doi.org/10.1186/s13660-020-02387-9

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Abstract

In this study, first, lacunary convergence of double sequences is introduced in fuzzy normed spaces, and basic definitions and theorems about lacunary convergence for double sequences are given in fuzzy normed spaces. Then, we introduce the concept of lacunary ideal convergence of double sequences in fuzzy normed spaces, and the relation between lacunary convergence and lacunary ideal convergence is investigated for double sequences in fuzzy normed spaces. Finally, in fuzzy normed spaces, we give the concept of limit point and cluster point for double sequences, and the theorems related to these concepts are given.

Highlights

Introduction and backgroundThe statistical convergence was derived from the convergence of real sequences by Fast [1] and Schoenberg [2]
Nanda [12] studied the sequences of fuzzy numbers again and S. enc. imen and Pehlivan [13] introduced the notions of a statistically convergent sequence and a statistically Cauchy sequence in a fuzzy normed linear space
We introduce and study the concepts of lacunary I2-convergence, lacunary convergence, FIθ2 -limit point, and FIθ2 -cluster point for double sequences in a fuzzy normed space

Summary

Introduction

Introduction and backgroundThe statistical convergence was derived from the convergence of real sequences by Fast [1] and Schoenberg [2]. We introduce and study the concepts of lacunary I2-convergence, lacunary convergence, FIθ2 -limit point, and FIθ2 -cluster point for double sequences in a fuzzy normed space.

Results

Conclusion