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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Also, we obtain the analogue of the well-known Dini's Theorem.
📌 3 Key Takeaways
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Objective & Hypothesis:In this article, we define the concept of $\Delta$-Cauchy$, \Delta$-uniform convergence and $\Delta$-pointwise convergence of a family of functions $\{f_{j}\}_{j\in \mathbb{J}}$, where $\mathbb{J}$ is a time scale.
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Key Findings & Data:We study the relationships between these notions.
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Conclusion & Impact:Also, we obtain the analogue of the well-known Dini's Theorem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$ \Delta $-Convergence · $ \Delta $-Cauchy · Statistical Convergence
Abstract
In this article, we define the concept of $\Delta$-Cauchy$, \Delta$-uniform convergence and $\Delta$-pointwise convergence of a family of functions $\{f_{j}\}_{j\in \mathbb{J}}$, where $\mathbb{J}$ is a time scale. We study the relationships between these notions. Moreover, we introduced sufficient conditions for interchangeability of $\Delta$-limitation with Riemann $\Delta$-integration or $\Delta$-differentiation. Also, we obtain the analogue of the well-known Dini's Theorem.
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Cite This Article
SEYYİDOĞLU, M. S., KARADAŞ, A. (2020). On $\Delta$-Uniform and $\Delta$-Pointwise Convergence on Time Scale. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 Sayı: 1, 218–225. https://ajindex.com/articles/920484