On the rates of approximation of Bernstein type operators

Asymptotic behavior of two Bernstein-type operators is studied in this paper. In the first case, the rate of convergence of a Bcrnstein operator for a bounded function f is studied at points x where f(x + ) and f( x-) exist. In the second case, the rate of convergence of a Szasz operator for a function f whose derivative is of bounded variation is studied at points x where f(x+) and f(x-) exist. Estimates of the rate of convergence are obtained For both cases and the estimates are the best possible for continuous points. (C) 2001 Academic Press.