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

Year 2020, Volume: 10 Issue: 1, 218 - 225, 25.06.2020

Mustafa Seyyit Seyyidoğlu Ayşe Karadaş

https://doi.org/10.37094/adyujsci.546724

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.

Keywords

$ \Delta $-Convergence, $ \Delta $-Cauchy, Statistical Convergence

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