- Adıyaman Üniversitesi Fen Bilimleri Dergisi
- Vol: 10 Issue: 1
- On $\Delta$-Uniform and $\Delta$-Pointwise Convergence on Time Scale
On $\Delta$-Uniform and $\Delta$-Pointwise Convergence on Time Scale
Authors : Mustafa Seyyit SEYYİDOĞLU, Ayşe KARADAŞ
Pages : 218-225
Doi:10.37094/adyujsci.546724
View : 20 | Download : 3
Publication Date : 2020-06-25
Article Type : Research
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