On the statistical and \(I\) variation of double sequences. (English) Zbl 1160.40003

Pratulananda, Das; Malik, Prasanta

Real Anal. Exch. 33(2007-2008), No. 2, 351-364 (2008).

Summary: We extend the notion of finite statistical variation of single sequences to double sequences using the double natural density of the set \(\mathbb{N} \times \mathbb{N}\). Certain consequences of this notion are investigated including its relation with statistical convergence introduced earlier. We also introduce the more general concept of \(I\) variation of double sequences and investigate its relation with \(I\) and \(I^*\) convergence.

MSC:

40B05	Multiple sequences and series
40A05	Convergence and divergence of series and sequences

Keywords:

double sequences; statistical convergence; statistical variation; \(I\)-variation; \(I\) and \(I^*\)-convergence