Strong converse inequalities for the weighted multivariate Bernstein-Durrmeyer operator on the simplex via multipliers

Abstract

It is demonstrated that multiplier methods naturally yield better constants in strong converse inequalities for the Bernstein-Durrmeyer operator. The absolute constants obtained in some of the inequalities are independent of the weight and the dimension. The estimates are stated in terms of the $K$-functional that is naturally associated to the operator.