$f$-Asymptotically $mathcal{I}_{sigmatheta}$-Equivalence of Real Sequences

Abstract

In this manuscript, we present the ideas of asymptotically $[{mathcal{I}_{sigmatheta}}]$-equivalence, asymptotically ${mathcal{I}_{sigmatheta}}(f)$-equivalence, asymptotically $[{mathcal{I}_{sigmatheta}}(f)]$-equivalence and asymptotically ${mathcal{I}(S_{sigmatheta})}$-equivalence for real sequences. In addition to, investigate some connections among these new ideas and we give some inclusion theorems about them.