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

Abstract

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.

Keywords

• Asymptotical Equivalence
• Deferred Cesàro Mean
• Difference Sequence
• Modulus Funtion
• Statistical Convergence

ρ. Mertebeden Modüllenmiş Ertelenmiş Ortalamalar Aracılığıyla Fark Dizilerinin Asimptotik İstatistiksel Eşdeğerliği Üzerine

Abstract

Bu çalışma, bir φ modulus fonksiyonu kullanarak ρ mertebeden Δ_φ^m-asimptotik ertelenmiş istatistiksel eşdeğerlik ve ρ mertebeden Δ_φ^m-asimptotik ertelenmiş kuvvetli Cesàro eşdeğerliği kavramlarını sunmaktadır. Çeşitli gerektirme teoremlerinin incelenmesinin yanı sıra, (u_n) and (v_n) dizileri ile ρ∈(0,1] parametresi üzerindeki belirli koşullar altında bu kavramlar arasındaki fonksiyonel ilişkiler analiz edilmektedir. Elde edilen sonuçlar; yüksek mertebeden fark operatörlerini, ertelenmiş aralıklar ve modulus tabanlı uzaklık ölçümleriyle birleştirerek mevcut literatürü genişletmektedir.

Keywords

• Asimptotik Eşdeğerlik
• Ertelenmiş Cesàro Ortalaması
• Fark Dizisi
• İstatistiksel Yakınsaklık
• Modülüs Fonksiyonu

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