Open Access
Translator Disclaimer
2013 The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces
XianFa Luo, JianYong Wang
Abstr. Appl. Anal. 2013(SI45): 1-6 (2013). DOI: 10.1155/2013/504076

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.

Citation

Download Citation

XianFa Luo. JianYong Wang. "The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces." Abstr. Appl. Anal. 2013 (SI45) 1 - 6, 2013. https://doi.org/10.1155/2013/504076

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1303.46016
MathSciNet: MR3132553
Digital Object Identifier: 10.1155/2013/504076

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.2013 • No. SI45 • 2013
Back to Top