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Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials

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Abstract

We establish the pointwise approximation theorems for the combinations of Bernstein polynomials by the rth Ditzian–Totik modulus of smoothness \( \omega ^{r}_{\Phi } (f,t) \)where Φ is an admissible step–weight function. An equivalence relation between the derivatives of these polynomials and the smoothness of functions is also obtained.

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Authors and Affiliations

  1. Department of Mathematics, Lishui University, Lishui 323000, P. R. China

    Lin Sen Xie

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  1. Lin Sen Xie
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Correspondence to Lin Sen Xie.

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The research is supported by Zhejiang Provincial Natural Science Foundation of China

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Xie, L.S. Pointwise Approximation Theorems for Combinations and Derivatives of Bernstein Polynomials. Acta Math Sinica 21, 1241–1248 (2005). https://doi.org/10.1007/s10114-004-0425-0

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  • DOI: https://doi.org/10.1007/s10114-004-0425-0

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