Univariate right fractional polynomial high order monotone approximation


Let f ε 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 [-0,1], 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).

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Demonstratio Mathematica