On the Rate of Convergence of the Generalized Durrmeyer Type Operators for Functions of Bounded Variation Original Research Article

In this paper we estimate the rate of convergence of the Durrmeyer–Bézier operators Dn, α(f, x) for functions of bounded variation and prove that the Dn, α(f, x) converge to the limit 1/(α+1) f(x+)+α/(α+1) f(x−) for functions of bounded variation f(t). Our result improves and extends the result of S. Guo (1987, J. Approx. Theory51, 183–192).