On the Statistical and I Variation of Double Sequences

Abstract

We extend the notion of finite statistical variation of single sequences by Faisant et al (2005) 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 by Mursaleen and Edely (2003). We also introduce the more general concept of $I$ variation of double sequences and investigate it's relation with $I$ and $I^*$ convergence.