Lacunary statistical convergence of double sequences and some inclusion results in n-normed spaces

Abstract

In this paper, we introduce the concept of lacunary statistical convergence of double sequences in n-normed spaces. Some inclusion relations between the sets of statistically convergent and lacunary statistically convergent cases of double sequences are established. In addition, we also define lacunary statistical Cauchy double sequences and prove that this notion is equivalent to the lacunary statistical convergence of double sequences.