Quantitative approximation by shift invariant multivariate sublinear-shilkret operators
A very general multivariate positive sublinear Shilkret integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized Shilkret operators are presented fulfilling all the above properties, the higher order of multivariate approximation of these operators is also considered. It follows .
Studies in Systems, Decision and Control
Anastassiou, G. (2019). Quantitative approximation by shift invariant multivariate sublinear-shilkret operators. Studies in Systems, Decision and Control, 190, 289-306. https://doi.org/10.1007/978-3-030-04287-5_14