论文标题
Korovkin定理的运营商版本；收敛程度及其应用
Operator version of Korovkin Theorem; Degree of Convergence and its Applications
论文作者
论文摘要
在最近的一篇文章中，Dumitru Popa证明了Korovkin定理的运营商版本。我们回想起O. Shisha和B. Mond于1968年获得的Korovkin定理的定量版本。在本文中，我们获得了Dumitru Popa获得的Korovkin定理的操作员版本的定量估计。我们还考虑了适用操作员版本并获得相似估计的各种示例，导致收敛程度。此外，我们通过证明定量版本获得了该结果的三角类似物。最后，我们将此结果应用于具有Toeplitz结构的大型线性系统的预处理问题。
In a recent article, Dumitru Popa proved an operator version of the Korovkin theorem. We recall the quantitative version of the Korovkin theorem obtained by O. Shisha and B. Mond in 1968. In this paper, we obtain a quantitative estimate for the operator version of the Korovkin theorem obtained by Dumitru Popa. We also consider various examples where the operator version is applicable and obtain similar estimates leading to the degree of convergence. In addition, we obtain the trigonometric analogue of this result by proving the quantitative version. Finally, we apply this result to the preconditioning problem of large linear systems with the Toeplitz structure.
