Multivariate Bernstein-Durrmeyer operators with arbitrary weight functions (Q968962)

The authors propose a class of Bernstein-Durrmeyer operators with respect to an arbitrary measure \(\rho\) on the \(d\)-dimensional simplex and a class of general polynomial integral operators with a kernel function involving Bernstein basis polynomials. These operators generalize the well-known Bernstein-Durrmeyer operators with respect to Jacobi weights. Some properties of the new operators are also investigated.