-functionals and multivariate Bernstein polynomials

Abstract: This paper estimates upper and lower bounds for the approximation rates of iterated Boolean sums of multivariate Bernstein polynomials. Both direct and inverse inequalities for the approximation rate are established in terms of a certain -functional. From these estimates, one can also determine the class of functions yielding optimal approximations to the iterated Boolean sums. [Copyright &y& Elsevier]