Statistically convergent double sequences
Copyright policy )Statistically convergent double sequences
In this aricle we introduce the notion of density of subsets of $ N \times N $. Using this concept we introduce the notion of statistically convergent double sequences and statistically Cauchy double sequences. The decomposition theorem is proved. The inclusion relations are obtained. We have shown that the bounded statistically convergent in Pringsheim's sense sequence space is not separable. A relation between strongly $ p $-Cesaro summability of double sequences and bounded statistically convergent double sequences is established.
Cauchy double sequences, density, sequence space, \(p\)-Cesàro summability, Convergence and divergence of series and sequences, Multiple sequences and series, Sequence spaces (including Köthe sequence spaces)
Cauchy double sequences, density, sequence space, \(p\)-Cesàro summability, Convergence and divergence of series and sequences, Multiple sequences and series, Sequence spaces (including Köthe sequence spaces)
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