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Higher order monotone approximation with linear di¤erential operators
AbstractLet f ∈ Cr([−1,1]), r ≥ 0 and let L* be a linear right fractional differential operator such that L*(f) ≥ 0 throughout [−1,0]. We can find a sequence of polynomials Qn of degree ≤ n such that L*(Qn) ≥ 0 over [−1,0], furthermore f is approximated right fractionally and simultaneously by Qn on [−1,1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for f(r).
Demonstratio Mathematica – de Gruyter
Published: Mar 1, 2016
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