Asymptotic behavior of two Bernstein-type operators is studied in this pape
r. 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 funct
ion 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 F
or both cases and the estimates are the best possible for continuous points
. (C) 2001 Academic Press.