Approximation by Positive Sublinear Operators

Abstract

Here we study the approximation of functions by positive sublinear operators under differentiability. We produce general Jackson type inequalities under initial conditions. We apply these to a series of well-known Max-product operators. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. It follows Anastassiou, Coroianu, Gal (J. Comput. Anal. Appl. 12(2):396–406, 2010, [3]).