In the present paper, we deal with some general estimates for the difference of operators which are associated with different fundamental functions. In order to exemplify the theoretical results presented in (for example) Theorem 2, we provide the estimates of the differences between some of the most representative operators used in Approximation Theory in especially the difference between the Baskakov and the Szasz–Mirakyan operators, the difference between the Baskakov and the Szasz–Mirakyan–Baskakov operators, the difference of two genuine-Durrmeyer type operators, and the difference of the Durrmeyer operators and the Lupas–Durrmeyer operators. By means of illustrative numerical examples, we show that, for particular cases, our result improves the estimates obtained by using the classical result of Shisha and Mond. We also provide the symmetry aspects of some of these approximations operators which we have studied in this paper.

中文翻译：

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高阶导数的一些正线性逼近算子的差异

在本文中，我们处理与不同基本函数相关的算子差异的一些一般估计。为了举例说明（例如）定理 2 中给出的理论结果，我们提供了近似理论中使用的一些最具代表性的算子之间差异的估计，特别是 Baskakov 和 Szasz-Mirakyan 算子之间的差异，差异Baskakov 和 Szasz-Mirakyan-Baskakov 算子之间的区别，两个真正的 Durrmeyer 类型算子的区别，以及 Durrmeyer 算子和 Lupas-Durrmeyer 算子的区别。通过说明性的数值例子，我们表明，对于特定情况，我们的结果改进了使用 Shisha 和 Mond 的经典结果获得的估计。