High order approximation 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. It follows (Anastassiou, Approximations by multivariate sublinear and max-product operators under convexity, submitted, 2017, ).
Studies in Systems, Decision and Control
Anastassiou, G. (2018). High order approximation by multivariate sublinear and max-product operators under convexity. Studies in Systems, Decision and Control, 147, 265-293. https://doi.org/10.1007/978-3-319-89509-3_12