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

Authors : Reha YAPALI, Husamettin COŞKUN

Pages : 24-31

Doi:10.33187/jmsm.1127905

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Publication Date : 2023-04-30

Article Type : Research Paper

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