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Univariate right fractional polynomial high order monotone approxi mation

Anastassiou G. A.

Demonstratio Mathematica

2016

Vol. 49, nr 1

1--10

Let (…) 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).