On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions, II
Copyright policy )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.
- Xiamen University China (People's Republic of)
Mathematics(all), Numerical Analysis, POLYNOMIALS, Bernstein-Kantorovich-Bézier type operators, Applied Mathematics, Approximation by positive operators, Rate of convergence, degree of approximation, Analysis, Bernstein-Bézier type operators
Mathematics(all), Numerical Analysis, POLYNOMIALS, Bernstein-Kantorovich-Bézier type operators, Applied Mathematics, Approximation by positive operators, Rate of convergence, degree of approximation, Analysis, Bernstein-Bézier type operators
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