On Asymptotically Statistical Equivalence of Difference Sequences via ρ-th Order Modulated Deferred Means

This study introduces the concepts of Δ_φ^m-asymptotically deferred statistical equivalence of order ρ and Δ_φ^m-asymptotically deferred strongly Cesaro equivalence of order ρ by utilizing a modulus function φ. Alongwith investigating several implication Theorems, we analyze the functional relationships between these concepts under specific conditions on the sequences (u_n) and (v_n) and the parameter ρ∈(0,1]. Our results extend the existing literature by merging higher-order difference operators with deferred intervals and modulus-based distance measures.