Univariate right fractional polynomial high order monotone approximation
Let 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]....
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-03-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2016.49.issue-1/dema-2016-0001/dema-2016-0001.xml?format=INT |
| _version_ | 1828383112666546176 |
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| author | Anastassiou George A. |
| author_facet | Anastassiou George A. |
| author_sort | Anastassiou George A. |
| collection | DOAJ |
| description | Let 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). |
| first_indexed | 2024-12-10T04:43:13Z |
| format | Article |
| id | doaj.art-871700bca1c048f9b66507edafc7c366 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-12-10T04:43:13Z |
| publishDate | 2016-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-871700bca1c048f9b66507edafc7c3662022-12-22T02:01:49ZengDe GruyterDemonstratio Mathematica2391-46612016-03-0149111010.1515/dema-2016-0001dema-2016-0001Univariate right fractional polynomial high order monotone approximationAnastassiou George A.0Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.Let 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.degruyter.com/view/j/dema.2016.49.issue-1/dema-2016-0001/dema-2016-0001.xml?format=INTmonotone approximationright Caputo fractional derivativeright fractional linear differential operatorhigher order modulus of smoothness26A3341A1041A1741A2541A2841A29 |
| spellingShingle | Anastassiou George A. Univariate right fractional polynomial high order monotone approximation Demonstratio Mathematica monotone approximation right Caputo fractional derivative right fractional linear differential operator higher order modulus of smoothness 26A33 41A10 41A17 41A25 41A28 41A29 |
| title | Univariate right fractional polynomial high order monotone approximation |
| title_full | Univariate right fractional polynomial high order monotone approximation |
| title_fullStr | Univariate right fractional polynomial high order monotone approximation |
| title_full_unstemmed | Univariate right fractional polynomial high order monotone approximation |
| title_short | Univariate right fractional polynomial high order monotone approximation |
| title_sort | univariate right fractional polynomial high order monotone approximation |
| topic | monotone approximation right Caputo fractional derivative right fractional linear differential operator higher order modulus of smoothness 26A33 41A10 41A17 41A25 41A28 41A29 |
| url | http://www.degruyter.com/view/j/dema.2016.49.issue-1/dema-2016-0001/dema-2016-0001.xml?format=INT |
| work_keys_str_mv | AT anastassiougeorgea univariaterightfractionalpolynomialhighordermonotoneapproximation |