Abstract
For a sequenceA = {Ak} ∞k−1 of positive constants letP A = {p(x): p(x) = Σ n k−1 a k x k ,n = 1,2, …, ¦a k ≦ A kk }. We consider the rate of approximation by elements ofP A , of continuous functions in [0, 1] which vanish at x = 0. Also a classP A is called “efficient” if globally it guarantees the Jackson rate of approximation. Some necessary conditions for efficiency and some sufficient ones are derived.
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Bak, J., v. Golitschek, M. & Leviatan, D. The rate of approximation by means of polynomials with restricted coefficients. Israel J. Math. 26, 265–275 (1977). https://doi.org/10.1007/BF03007646
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DOI: https://doi.org/10.1007/BF03007646