In this paper, we study the order of approximation with respect to the Jordan variation for the generalized and the Kantorovich sampling series, based upon averaged type kernels. In particular, we establish some quantitative estimates for the above operators. For the latter purpose, we introduce a suitable modulus of smoothness in the space of absolutely continuous functions on the whole real line.

中文翻译：

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样本类型算子关于约旦变异的定量估计

在本文中，我们研究了基于平均类型核的广义采样序列和Kantorovich采样序列的约旦变异的近似阶数。特别是，我们为上述算子建立了一些定量估计。出于后一个目的，我们在整个实线上的绝对连续函数的空间中引入了合适的平滑系数。