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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Vydáno v:Abstract and Applied Analysis Ročník 2014; s. 770 - 779-671
Hlavní autoři: Bing-Zheng Li, Ding-Xuan Zhou
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Hindawi Limiteds 01.12.2014
John Wiley & Sons, Inc
Témata:
Banach spaces
Error analysis
Mathematical functions
Theory
ISSN:1085-3375, 1687-0409
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/454375