Approximations by multivariate sublinear and Max-product operators under convexity
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-Szász-Mirakjan type, of Baskakov 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 assumption.
Anastassiou, G. (2018). Approximations by multivariate sublinear and Max-product operators under convexity. Demonstratio Mathematica, 51 (1), 85-105. https://doi.org/10.1515/dema-2018-0008