Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation

First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions

“…In particular, (12) is true for f ∈ DBV [0, 1] (that is, f is differentiable function whose derivative is of bounded variation, cf. [3]), since the class of functions DBV [0, 1] is a subclass of the class Φ DB . We also point out that Abel [1] presented the complete asymptotic expansion for the operators M n under much stronger conditions.…”

“…[3], [4], [6]- [9], [11]- [13]). In this paper we give a sharp estimate for the first order absolute moment of the operators M n .…”

On the Rates of Approximation of Bernstein Type Operators

“…As far as the rate of convergence of Bernstein operator for |t&x| is concerned, Bojanic and Cheng [2] proved the following asymptotic form:…”

Blending type approximation by bézier-summation-integral type operators

“…In these works, the direct approximation results were obtained and the rate of convergence for functions of bounded variation were established. The order of approximation of the summation-integral type operators for functions with derivatives of bounded variation is estimated in [1,4,6,7,14,15,16,17,18,21,20,22,25]. To express our results we give the following auxiliary results.…”