Univariate left fractional polynomial high order monotone approximation

Abstract

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).

Publication Title

Bulletin of the Korean Mathematical Society

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