论文标题
在Banach功能空间中重新访问Korovkin型定理
Revisiting Korovkin-type Theorems in Banach Function Spaces
论文作者
论文摘要
根据Yusuf Zeren等人确定的Banach函数空间中的Korovkin型定理。 （2022）。我们证明，在该定理中，操作员的积极性不是必要的要求，并提供了适用的非正面操作员的示例。在积极性的假设下，我们建立了结果的运算符版本。此外，我们使用连续性模量得出结果的定量形式。我们将结果应用于诸如Lebesgue空间，加权Lebesgue空间，Grand Lebesgue Space等示例。此外，我们为特定情况提供了数值插图。
This article delves into Korovkin-type theorems in Banach function spaces, as established by Yusuf Zeren et al. (2022). We prove that in this theorem, the positivity of the operators is not a necessary requirement and provide example of a non positive operator where it is applicable. Under the assumption of positivity, we establish an operator version of the result. Additionally, we derive a quantitative form of the result using the modulus of continuity. We apply the result to examples such as Lebesgue space, Weighted Lebesgue space, Grand Lebesgue space, etc. Furthermore, we present numerical illustrations for specific cases.
