Abstract. For the simplex $S$ and a Jacobi-type weight the Bernstein-Durrmeyer operators will be given and their properties investigated. A direct estimate and a matching strong converse inequality will be derived.

AMS Subject Classification (1991): 41A36, 41A25, 41A63

Keyword(s): Multivariate Jacobi polynomials, Bernstein--Durrmeyer operators, direct and converse inequalities

Received April 7, 1994. (Registered under 5629/2009.)