On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation

in this paper we estimate the rate of convergence of the Durrmeyer-Bezier operators D-n,D-alpha (f,x) for functions of bounded variation and prove that the D-n,D-alpha (f,x) converge to the limit 1/(alpha + 1)f(x+) + alpha/(alpha + 1) f(x-) for functions of bounded variation f(t). Our result improves and extends the result of S. Guo (1987. J, Approx. Theory 51, 183-192).(C) 2000 Academic Press.