Lacunary invariant and lacunary invariant statistical equivalence of order ? for double set sequences

In this paper, for double set sequences, the concepts of asymptotical lacunary invariant equivalence and asymptotical lacunary invariant statistical equivalence of order β (0 < β ≤ 1) in the Wijsman sense were introduced. Also, some properties of these new equivalence concepts and the relations between them were investigated.