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

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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.

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Acknowledgements

The authors express their gratitude to the anonymous referee for excellent comments and suggestions, which have enormously enhanced the quality and presentation of this paper.

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Correspondence to Bipan Hazarika.

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Hazarika, B., Savas, E. Lacunary statistical convergence of double sequences and some inclusion results in n-normed spaces. Acta Math Vietnam. 38, 471–485 (2013). https://doi.org/10.1007/s40306-013-0028-x

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