Abstract
Theorem 1 gives an estimate for the approximation of a continuous functionf by polynomials resulting from the convolution off with non-negative algebraic polynomialsp n . Jackson's theorem can be deduced from it by choosing a particularp n whose second Chebyshev-Fourier coefficient is sufficiently close to −1.
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References
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Work supported in part by the Atomic Energy Commission under contract U.S. AEC AT (11-1) 1469, and in part by the National Science Foundation under grant NSF-GJ-812.
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Chawla, M.M. Approximation by non-negative algebraic polynomials. BIT 10, 243–248 (1970). https://doi.org/10.1007/BF01934195
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DOI: https://doi.org/10.1007/BF01934195