Abstract
As is known, if \(f\in C^2[0,1]\), then, for the Bernstein operator \(B_n\), there holds
uniformly on [0, 1]. We characterize the rate of this convergence in terms of K-functionals and moduli of smoothness.
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This work was supported by Grant DN 02/14 of the Fund for Scientific Research of the Bulgarian Ministry of Education and Science.
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Draganov, B.R., Gadjev, I. Direct and Converse Voronovskaya Estimates for the Bernstein Operator. Results Math 73, 11 (2018). https://doi.org/10.1007/s00025-018-0795-8
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DOI: https://doi.org/10.1007/s00025-018-0795-8
Keywords
- Bernstein polynomials
- direct estimate
- converse estimate
- Voronovskaya inequality
- modulus of smoothness
- K-functional