High Order Approximation by Multivariate Sublinear and Max-Product Operators Under Convexity

Abstract

Here we search quantitatively under convexity 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-Szasz-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 which fulfills a convexity assumption. It follows (Anastassiou, Approximations by multivariate sublinear and max-product operators under convexity, submitted, 2017, [4]).