On Ideal Version of Lacunary Statistical Convergence of Double Sequences

For any double lacunary sequence θ_rs = {(kr, ls)} and an admissible ideal I2 ⊆ P(N × N), the aim of present work is to define the concepts of Nθrs (I2)− and Sθrs (I2)−convergence for double sequence of numbers. We also present some inclusion relations between these notions and prove that Sθrs (I2)∩L^ 2 ∞ and S2(I2) ∩L 2 ∞ are closed subsets of L^2 ∞, the space of all bounded double sequences of numbers.