Asymptotically lacunary I_σ-equivalence of sequences of sets

Abstract

In this study, we introduce the notions of Wijsman asymptotically strongly p-lacunary invariant equivalence ([W_(N_σθ)^L ]_p), Wijsman asymptotically lacunary I-invariant equivalence (W_(I_σθ)^L) and Wijsman asymptotically lacunary I^*-invariant equivalence (W_(I_σθ^*)^L) for sequences of sets. Also, the relationships among the notions of Wijsman asymptotically lacunary invariant equivalence, Wijsman asymptotically lacunary invariant statistical equivalence, [W_(N_σθ)^L ]_p, W_(I_σθ)^L and W_(I_σθ^*)^L are investigated.