Overiteration of $d$-variate tensor product Bernstein operators: a quantitative result

Abstract

Extending an earlier estimate for the degree of approximation of overiterated univariate Bernstein operators towards the same operator of degree one, it is shown that an analogous result holds in the $d$-variate case. The method employed can be carried over to many other cases and is not restricted to Bernstein-type or similar methods.