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

TL;DR

This paper improves strong converse inequalities for the weighted multivariate Bernstein-Durrmeyer operator on the simplex by using multiplier methods, achieving better constants independent of weight and dimension, with estimates based on the $K$-functional.

Contribution

It introduces multiplier methods to derive sharper constants in inequalities for the Bernstein-Durrmeyer operator, independent of weight and dimension.

Findings

Constants in inequalities are independent of weight and dimension.

Multiplier methods yield better constants in strong converse inequalities.

Estimates are expressed via the $K$-functional associated with the operator.

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.