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 : 30 | Download : 12

Publication Date : 2020-06-25

Article Type : Research Paper

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