Analysis of Approximation by Linear Operators on Variable Lρp(·) Spaces and Applications in Learning Theory

Bing-Zheng Li and Ding-Xuan Zhou

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: This paper is concerned with approximation on variable Lρp(·) spaces associated with a general exponent function p and a general bounded Borel measure ρ on an open subset Ω of Rd. 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 Lρp(·) 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)
https://doi.org/10.1155/2014/454375

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:wly:jnlaaa:v:2014:y:2014:i:1:n:454375

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().