On $\Delta$-Uniform and $\Delta$-Pointwise Convergence on Time Scale

On $\Delta$-Uniform and $\Delta$-Pointwise Convergence on Time Scale

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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Adıyaman Üniversitesi Fen Bilimleri Dergisi-Cover
  • Yayın Aralığı: 2
  • Başlangıç: 2011
  • Yayıncı: Adıyaman Üniversitesi