On the $Δ _{{Λ ^2}}^f$-Statistical Convergence on Product Time Scale - Metin Basarır; Bayram Sözbir; Selma Altundağ (Universal Journal of Mathematics and Applications, 2020)
In this paper, we first define a new density of a $Δ $-measurable subset of a product time scale ${Λ ^2}$ with respect to an unbounded modulus function. Then, by using this definition, we introduce the concepts of $Δ _{{Λ ^2}}^f$-statistical convergence and $Δ _{{Λ ^2}}^f$-statistical Cauchy for a $Δ $-measurable real-valued function defined on product time scale ${Λ ^2}$ and also obtain some results about these new concepts. Finally, we present the definition of strong $Δ _{{Λ ^2}}^f$-Cesaro summability on ${Λ ^2}$ and investigate the connections between these new concepts.