Triple Sequences and Their Statistical Convergence


Pringsheim gave the definition of the convergence for double sequences in 1900. The idea of statistical convergence was first presented by Fast in 1951. In 2003 Tripathy and Mursaleen introduced statistical convergence of double sequences. In this article we introduce the notions of triple sequences and statistically convergent triple sequence. We also introduce the notions of statistical Cauchy for triple sequences, a necessary and sufficient condition for a triple statistical Cauchy sequence to be a convergent triple sequence is given.


Double sequence; triple sequence; statistical convergence; triple natural density.

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