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Univariate right fractional polynomial high order monotone approximation

Univariate right fractional polynomial high order monotone approximation AbstractLet f ∈ 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 [−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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

Univariate right fractional polynomial high order monotone approximation

Demonstratio Mathematica , Volume 49 (1): 10 – Mar 1, 2016

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References (12)

Publisher
de Gruyter
Copyright
© 2016 George A. Anastassiou, published by De Gruyter Open
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2016-0001
Publisher site
See Article on Publisher Site

Abstract

AbstractLet f ∈ 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 [−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).

Journal

Demonstratio Mathematicade Gruyter

Published: Mar 1, 2016

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