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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2020 / Cilt: 10 - Sayı: 1

On Δ-Uniform and Δ-Pointwise Convergence on Time Scale

Zaman Skalası Üzerinde Δ-Düzgün ve Δ-Noktasal Yakınsaklık

Ayşe KARADAŞ
Mustafa Seyyit SEYYİDOĞLU
Pages
218–225
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

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

Keywords: Δ-Convergence; Δ-Cauchy; Statistical convergence.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we define the concept of Δ-Cauchy, Δ-uniform convergence and Δpointwise convergence of a family of functions {f}f∈j, where j is a time scale.
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Key Findings & Data:We study the relationships between these notions.
💡
Conclusion & Impact:Keywords: Δ-Convergence; Δ-Cauchy; Statistical convergence.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this article, we define the concept of Δ-Cauchy, Δ-uniform convergence and Δpointwise convergence of a family of functions {f}f∈j, where j is a time scale. We study the relationships between these notions. Moreover, we introduced sufficient conditions for interchangeability Δ-limitation with Riemann Δ-integration or Δ-differentiation. Also, we obtain the analogue of the well-known Dini's Theorem. Keywords: Δ-Convergence; Δ-Cauchy; Statistical convergence.

Özet

Bu makalede j bir zaman skalası olmak üzere, {fj}j∈j fonksiyon ailesi için Δ-Cauchy, Δdüzgün yakınsaklık ve Δ-noktasal yakınsaklık kavramları verilerek bu kavramlar arasındaki ilişkiler incelenmiştir. Δ-limit ile Riemann Δ-integrali ve Δ-türevin yer değişme problemi araştırılarak Dini Teoreminin farklı bir versiyonu elde edilmiştir. Anahtar Kelimeler: Δ-Yakınsaklık; Δ-Cauchy; İstatistiksel yakınsaklık.

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Cite This Article

KARADAŞ, A., SEYYİDOĞLU, M. S. (2022). On Δ-Uniform and Δ-Pointwise Convergence on Time Scale. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 - Sayı: 1, 218–225. https://ajindex.com/articles/428454

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