Asymptotically I-Cesaro equivalence of sequences of sets

Abstract

In this paper, we defined concepts of asymptotically $\mathcal{I}$-Cesaro equivalence and investigate the relationships between the concepts of asymptotically strongly $\mathcal{I}$-Cesaro equivalence, asymptotically strongly $\mathcal{I}$-lacunary equivalence, asymptotically $p$-strongly $ \mathcal{I}$-Cesaro equivalence and asymptotically $\mathcal{I}$-statistical equivalence of sequences of sets.