Asymptotically lacunary I_σ-equivalence of sequences of sets

Abstract

In this study, we introduce the concepts of Wijsman p-strongly asymptotically lacunary invariant equivalence ([W_{N_{θσ}}^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 concepts of Wijsman asymptotically lacunary invariant equivalence, Wijsman asymptotically lacunary invariant statistical equivalence, [W_{N_{θσ}}^L ]_p, W_{I_{σθ}}^L and W_{I_{σθ}^*}^L were investigated.