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Journals / Muş Alparslan Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 14 Sayı: 1

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

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

Fatih Temizsu(SIVAS SCIENCE AND TECHNOLOGY UNIVERSITY, FACULTY OF ENGINEERING AND NATURAL SCIENCES)0000-0001-8929-5973
Pages
202–208
Publication Date
2026-06-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our results extend the existing literature by merging higher-order difference operators with deferred intervals and modulus-based distance measures.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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].
💡
Conclusion & Impact:Our results extend the existing literature by merging higher-order difference operators with deferred intervals and modulus-based distance measures.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Asimptotik Eşdeğerlik · Ertelenmiş Cesàro Ortalaması · Fark Dizisi

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.

Özet

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.

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Cite This Article

Temizsu, F. (2026). On Asymptotically Statistical Equivalence of Difference Sequences via ρ-th Order Modulated Deferred Means. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, Cilt: 14 Sayı: 1, 202–208. https://doi.org/10.18586/msufbd.1947226

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