f$-Asymptotically $\mathcal{I}_{\sigma\theta}$-Equivalence of Real Sequences

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