Abstract and Applied Analysis

The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces

XianFa Luo and JianYong Wang

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Abstract

Let C be a closed bounded convex subset of a real Banach space X with 0 as its interior and p C the Minkowski functional generated by the set C . For a nonempty set G in X and x X , g 0 G is called the generalized best approximation to x from G if p C ( g 0 x ) p C ( g x ) for all g G . In this paper, we will give a distance formula under p C from a point to a closed hyperplane H ( x , α ) in X determined by a nonzero continuous linear functional x in X and a real number α, a representation of the generalized metric projection onto H ( x , α ) , and investigate the continuity of this generalized metric projection, extending corresponding results for the case of norm.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 504076, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449680

Digital Object Identifier
doi:10.1155/2013/504076

Mathematical Reviews number (MathSciNet)
MR3132553

Zentralblatt MATH identifier
1303.46016

Citation

Luo, XianFa; Wang, JianYong. The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 504076, 6 pages. doi:10.1155/2013/504076. https://projecteuclid.org/euclid.aaa/1393449680


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