Analysis of Approximation by Linear Operators on Variable Spaces and Applications in Learning Theory

Bing-Zheng Li and Ding-Xuan Zhou

Abstract and Applied Analysis, 2014, vol. 2014, 1-10

Abstract:

This paper is concerned with approximation on variable spaces associated with a general exponent function and a general bounded Borel measure on an open subset of . We mainly consider approximation by Bernstein type linear operators. Under an assumption of log-Hölder continuity of the exponent function , we verify a conjecture raised previously about the uniform boundedness of Bernstein-Durrmeyer and Bernstein-Kantorovich operators on the 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.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2014/454375.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2014/454375.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:454375

DOI: 10.1155/2014/454375

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().