Construction of Stancu-type Bernstein operators based on Bézier bases with shape parameter \(\lambda\). (English) Zbl 1423.41022
Summary: We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter \(\lambda \in [- 1, 1]\) and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type \(\lambda\)-Bernstein operators and study their approximation behaviors.
MSC:
| 41A25 | Rate of convergence, degree of approximation |
| 41A35 | Approximation by operators (in particular, by integral operators) |
Keywords:
Stancu-type Bernstein operators; Bézier bases; Voronovskaja-type theorems; modulus of continuity; rate of convergence; bivariate operators; approximation propertiesReferences:
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