Abstract

In the present article, we extend our study of Kantorovich type exponential sampling operators introduced in [4]. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional. Further, we improve the order of approximation by using the convex type linear combinations of these operators. Finally, we provide few examples of kernels along with the graphical representations.

中文翻译：

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关于 Kantorovich 指数采样算子的逼近

摘要

在本文中，我们扩展了对 [4] 中介绍的 Kantorovich 型指数采样算子的研究。我们根据适当的 K 泛函推导出 Voronovskaya 类型定理及其对这些算子的定量估计。此外，我们通过使用这些算子的凸型线性组合来提高逼近的阶数。最后，我们提供了几个内核示例以及图形表示。