UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION
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Let f ∈ Cr ([−1, 1]), r ≥ 0 and let L∗ be a linear left fractional differential operator such that L∗ (f) ≥ 0 throughout [0, 1]. We can find a sequence of polynomials Qn of degree ≤ n such that L∗ (Qn) ≥ 0 over [0, 1], furthermore f is approximated left 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).
Abstract
Let f ∈ Cr ([−1, 1]), r ≥ 0 and let L∗ be a linear left fractional differential operator such that L∗ (f) ≥ 0 throughout [0, 1]. We can find a sequence of polynomials Qn of degree ≤ n such that L∗ (Qn) ≥ 0 over [0, 1], furthermore f is approximated left 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).
참고문헌 (6)
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