关于二元Kantorovich指数抽样序列
On Bivariate Kantorovich Exponential Sampling Series
摘要：
本文分析了Kantorovich型指数抽样序列族的二元推广的逼近性质。我们推导出这些采样类型系列的逐点和Voronovskaya型定理。利用光滑模，得到了这类级数收敛阶的定量估计。进一步，我们建立了这些级数的逼近阶与广义布尔和（GBS）算子。最后，我们提供了几个例子的内核的理论可以应用随着图形表示和误差估计。
英文摘要：
We analyse the approximation properties of the bivariate generalization of the family of Kantorovich type exponential sampling series. We derive the point-wise and Voronovskaya type theorem for these sampling type series. Using the modulus of smoothness, we obtain the quantitative estimate of order of convergence of these series. Further, we establish the degree of approximation for these series associated with generalized Boolean sum (GBS) operators. Finally, we provide a few examples of kernels to which the theory can be applied along with the graphical representation and error estimates.
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