High Order Approximation by Sublinear and Max-Product Operators Using Convexity

Abstract

Here we consider quantitatively using convexity the approximation of a function by general positive sublinear operators with applications to Max-product operators. These are of Bernstein type, of Favard–Szász–Mirakjan type, of Baskakov type, of Meyer–Köning and Zeller type, of sampling type, of Lagrange interpolation type and of Hermite–Fejér 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 property. It follows Anastassiou (Approximation by Sublinear and Max-product Operators using Convexity, 2017, [6]).