Univariate left fractional polynomial high order monotone approximation
Let f Î Cr ([−1, 1]), r ³0 and let L∗ be a linear left frac- tional differential operator such that L∗ (f) ³ 0 throughout [0, 1]. We can find a sequence of polynomials Qn of degree £ n such that L∗ (Qn) ³ 0 over [0, 1], furthermore f is approximated left fractionally and simulta- neously 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).
Bulletin of the Korean Mathematical Society
Anastassiou, G. (2015). Univariate left fractional polynomial high order monotone approximation. Bulletin of the Korean Mathematical Society, 52 (2), 593-601. https://doi.org/10.4134/BKMS.2015.52.2.593