In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series $$(I_{w}^{\chi })_{w>0}.$$ ( I w χ ) w > 0 . Further, we establish a representation formula and an inverse result of approximation for these operators. Finally, we give some examples of kernel functions to which the theory can be applied along with the graphical representation.

中文翻译：

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Kantorovich 型指数采样序列的正反结果

在本文中，我们分析了 Kantorovich 型指数采样序列的新族的行为。我们为 $$(I_{w}^{\chi })_{w>0}.$$ ( I w χ ) w > 0 级数推导出逐点逼近定理和 Voronovskaya 型定理。此外，我们为这些算子建立了一个表示公式和一个近似的逆结果。最后，我们给出了一些核函数的例子，该理论可以与图形表示一起应用于这些核函数。