Sharp error estimates for multivariate positive linear operators which reproduce the linear polynomials
Shayne F. D. Waldron · ResearchSpace (University of Auckland) · 1997
A sharp pointwise error estimate is given for multivariate positive linear operators which reproduce the linear polynomials. This quantitative Korovkin--type theorem generalises a known univariate result. It is applied to a number of operators including the multivariate Bernstein operators, and the recently introduced Bernstein--Schoenberg type operators of Dahmen, Micchelli and Seidel.