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In the present paper we introduce some new sequence spaces in the n-normed space. We define here some new spaces of double sequences by using the notions of lacunary sequences, difference sequences, almost convergence, sequence of Orlicz functions and statistical convergence. We examine some topological properties of these spaces of double sequences, inclusion relations between these newly defined sequence spaces and establish relation with lacunary statistical convergence. The study of these new sequence spaces provides a tool to deal with convergence problems of double sequences. 2010 Mathematics Subject Classification: 40A05; 46A45; 46B70

Some spaces of difference sequences and lacunary statistical convergence in $n$-normed space defined by sequence of Orlicz functions