Analysis of Approximation by Linear Operators on Variable L_p^(p(．)) Spaces and Applications in Learning Theory
This paper is concerned with approximation on variable [superscript] L ρ p ( · ) [/superscript] spaces associated with a general exponent function p and a general bounded Borel measure ρ on an open subset Ω of [superscript] R d [/superscript] . We mainly consider approximation by Bernstein type line...
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| Veröffentlicht in: | Abstract and Applied Analysis Jg. 2014; S. 770 - 779-671 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Hindawi Limiteds
01.12.2014
John Wiley & Sons, Inc |
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| ISSN: | 1085-3375, 1687-0409 |
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| Abstract | This paper is concerned with approximation on variable [superscript] L ρ p ( · ) [/superscript] spaces associated with a general exponent function p and a general bounded Borel measure ρ on an open subset Ω of [superscript] R d [/superscript] . We mainly consider approximation by Bernstein type linear operators. Under an assumption of log-Hölder continuity of the exponent function p , we verify a conjecture raised previously about the uniform boundedness of Bernstein-Durrmeyer and Bernstein-Kantorovich operators on the [superscript] L ρ p ( · ) [/superscript] space. Quantitative estimates for the approximation are provided for high orders of approximation by linear combinations of such positive linear operators. Motivating connections to classification and quantile regression problems in learning theory are also described. |
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| AbstractList | This paper is concerned with approximation on variable [superscript] L ρ p ( · ) [/superscript] spaces associated with a general exponent function p and a general bounded Borel measure ρ on an open subset Ω of [superscript] R d [/superscript] . We mainly consider approximation by Bernstein type linear operators. Under an assumption of log-Hölder continuity of the exponent function p , we verify a conjecture raised previously about the uniform boundedness of Bernstein-Durrmeyer and Bernstein-Kantorovich operators on the [superscript] L ρ p ( · ) [/superscript] space. Quantitative estimates for the approximation are provided for high orders of approximation by linear combinations of such positive linear operators. Motivating connections to classification and quantile regression problems in learning theory are also described. |
| Author | Bing-Zheng Li Ding-Xuan Zhou |
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| ContentType | Journal Article |
| Copyright | Copyright © 2014 Bing-Zheng Li and Ding-Xuan Zhou. Bing-Zheng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| DOI | 10.1155/2014/454375 |
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| SubjectTerms | Banach spaces Error analysis Mathematical functions Theory |
| Title | Analysis of Approximation by Linear Operators on Variable L_p^(p(．)) Spaces and Applications in Learning Theory |
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