High-order approximation by multivariate shift-invariant convolution type operators

High order differential functions of several variables are approximated by multivariate shift-invariant convolution type operators and their generalizations. The high order of this approximation is determined by giving some multivariate Jackson-type inequalities, engaging the first multivariate usual modulus of continuity of the Nth-order partial derivatives of the multivariate function under approximation. © 2004 Elsevier Ltd. All rights reserved