Abstract

In this paper, by using regular summability methods we modify the Bernstein–Chlodovsky operators in order get more general and powerful results than the classical aspects. We study Korovkin-type approximation theory on weighted spaces. As a special case, it is possible to Cesàro approximate (arithmetic mean convergence) to the test function $e_2(x)=x^2$ although it fails for the classical Bernstein–Chlodovsky operators. At the end of the paper, we extend our results to the multi-dimensional case.

中文翻译：

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Bernstein-Chlodovsky 算子近似中的一般可和性方法

摘要

在本文中，通过使用常规可和性方法，我们修改了 Bernstein-Chlodovsky 算子，以获得比经典方面更通用和更强大的结果。我们研究加权空间上的 Korovkin 型逼近理论。作为一种特殊情况，可以将 Cesàro 逼近（算术平均收敛）到测试函数${\mathrm{电子}}_2(X)=X^2$尽管它对于经典的 Bernstein-Chlodovsky 算子失败了。在论文的最后，我们将结果扩展到多维情况。