High Order Approximation by Multivariate Sublinear and Max-Product Operators

Abstract

Here we study quantitatively the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators. These are of Bernstein type, of Favard–Sz asz–Mirakjan type, of Baskakov type, of sampling type, of Lagrange interpolation type and of Hermite–Fejer interpolation type. Our results are both: under the presence of smoothness and without any smoothness assumption on the function to be approximated. It follows (Anastassiou, Approximation by Multivariate Sublinear and Max-Product Operators, 2017, submitted, [4]).