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Analysis of Approximation by Linear Operators on Variable L ρ p ( · ) Spaces and Applications in Learning Theory
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-16
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
This paper is concerned with approximation on variable L ρ p ( · ) spaces associated with a general exponent function p and a general bounded Borel measure ρ on an open subset Ω of R d .
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 L ρ p ( · ) 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.
American Psychological Association (APA)
Li, Bing-Zheng& Zhou, Ding-Xuan. 2014. Analysis of Approximation by Linear Operators on Variable L ρ p ( · ) Spaces and Applications in Learning Theory. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1033767
Modern Language Association (MLA)
Li, Bing-Zheng& Zhou, Ding-Xuan. Analysis of Approximation by Linear Operators on Variable L ρ p ( · ) Spaces and Applications in Learning Theory. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1033767
American Medical Association (AMA)
Li, Bing-Zheng& Zhou, Ding-Xuan. Analysis of Approximation by Linear Operators on Variable L ρ p ( · ) Spaces and Applications in Learning Theory. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1033767
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033767