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

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.