Abstract
Because all the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange–Hermite interpolation formula, in this paper we obtain semi-discrete quantitative Voronovskaya-type theorems based on various other Lagrange–Hermite interpolation formulas. Applications to Bernstein–Kantorovich and to Bernstein operators are presented.
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Gal, S.G. Semi-discrete Quantitative Voronovskaya-Type Theorems for Positive Linear Operators. Results Math 75, 117 (2020). https://doi.org/10.1007/s00025-020-01236-x
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DOI: https://doi.org/10.1007/s00025-020-01236-x
Keywords
- Lagrange–Hermite interpolation
- positive linear operators
- quantitative semi-discrete Voronovskaya results
- modulus of continuity
- Bernstein–Kantorovich polynomials
- Bernstein polynomials