Lacunary Statistical Convergence for Double Sequences on $\mathscr{L}-$ Fuzzy Normed Space

Year 2023, Volume: 6 Issue: 1, 24 - 31, 30.04.2023

Reha Yapalı Husamettin Coşkun

https://doi.org/10.33187/jmsm.1127905

Cited By: 2

Abstract

On $\mathscr{L}-$ fuzzy normed spaces, which is the generalization of fuzzy spaces, the notion of lacunary statistical convergence for double sequences which is a generalization of statistical convergence, are studied and developed in this paper. In addition, the definitions of lacunary statistical Cauchy and completeness for double sequences and related theorems are given on $\mathscr{L}-$ fuzzy normed spaces. Also, the relationship of lacunary statistical Cauchyness and lacunary statistical boundedness for double sequences with respect to $\mathscr{L}-$ fuzzy norm is shown.

Keywords

L −fuzzy normed space, Lacunary double sequences, Lacunary statistically convergence, Lacunary statistical boundedness, Lacunary statistical Cauchy

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