A best constant for bivariate Bernstein and Szasz-Mirakyan operators

For classical Bernstein operators over the unit square, we obtain the best uniform constant in preservation of the usual l(infinity)-modulus of continuity, at the same time we show that it coincides with the corresponding best uniform constant for bivariate Szasz operators. The result validates a conjecture stated in a previous paper. The proof involves both probabilistic and analytic arguments, as well as numerical computation of some specific values. (C) 2003 Elsevier Science (USA). All rights reserved.