Invariant and lacunary invariant statistical equivalence of order β for double set sequences

Abstract

In this study, as a new approach to the concept of asymptotical equivalence in the Wijsman sense for double set sequences, the new concepts which are called asymptotical invariant statistical equivalence of order β and asymptotical lacunary invariant statistical equivalence of order β (0 < β ≤ 1) in the Wijsman sense for double set sequences are introduced and explained with examples. In addition, the existence of some relations between these concepts and furthermore, the relationships between these concepts and previously studied asymptotical equivalence concepts in the Wijsman sense for double set sequences are investigated.