On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions. II
For Bernstein-Bézier type operators \(B_n^{(\alpha)}\), \(n \in \mathbb{N}_0\), \(0<\alpha<1\) and Bernstein-Kantorovich-Bézier type operators \(L_n^{(\alpha)}\), \(n\in\mathbb{N}_0\), \(0<\alpha<1\) the pointwise rate of convergence of \(B_n^{(\alpha)}f\) and \(L_n^{(\alpha)}f\) respectively for \(n\to \infty\) to functions \(f\in BV[0,1]\) is studied. The estimates turn out to be asymptotically optimal. In a first paper \textit{X. Zeng}, and \textit{A. Piriou} [J. Approximation Theory 95, No. 3, 369-387 (1998; Zbl 0918.41016) the case \(\alpha\geq 1\) has been treated.
Bernstein-Kantorovich-Bézier type operators
scientific article; zbMATH DE number 1496282