In this paper we study the problem of the convergence in variation for the generalized sampling series based upon averaged-type kernels in the multidimensional setting. As a crucial tool, we introduce a family of operators of sampling-Kantorovich type for which we prove convergence in L p on a subspace of L p (R N ): therefore we obtain the convergence in variation for the multidimensional generalized sampling series by means of a relation between the partial derivatives of such operators

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... on an absolutely continuous function f and the sampling-Kantorovich type operators acting on the partial derivatives of f . Applications to digital image processing are also furnished. https://doi.org/10.5186/aasfm.2020.4532 2010 Mathematics Subject Classification: Primary 41A30, 41A05.