On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions
Copyright policy )On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions
For Bernstein-Bézier type operators \(B_n^{(\alpha)}\), \(\alpha \geq 1\) and Bernstein-Kantorovich-Bézier type operators \(L_n^{(\alpha)}\) the pointwise rate of convergence of \(B_n^{(\alpha)}f\) and \(L_n^{(\alpha)}f\) respectively to functions \(f\in BV[0,1]\) (which are not necessarily normalized) is studied. The estimates turn out to be optimal when \(n\to\infty\) for continuity points and points of discontinuity of \(f\in BV[0,1]\).
- Xiamen University China (People's Republic of)
- Laboratoire de Mathématiques France
- Nice Sophia Antipolis University France
- Université Côte d'Azur France
Mathematics(all), Numerical Analysis, functions of bounded variation, Bernstein-Kantorovich-Bézier type operators, Applied Mathematics, Approximation by positive operators, Rate of convergence, degree of approximation, Analysis
Mathematics(all), Numerical Analysis, functions of bounded variation, Bernstein-Kantorovich-Bézier type operators, Applied Mathematics, Approximation by positive operators, Rate of convergence, degree of approximation, Analysis
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