On generalized ideal asymptotically statistical equivalent of order $α$ for functions

Abstract

We introduce new definitions related to the notions of asymptotically $\mathcal{I}_{\lambda}$ -statistical equivalent of order \alpha to multiple L and strongly $\mathcal{I}_{\lambda}$ -asymptotically equivalent of order $\alpha$ to multiple $L$ by using two nonnegative real-valued Lebesque measurable functions in the interval $(1,\infty )$ instead of sequences. In addition, we also present some inclusion theorems.