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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 504076, 6 pages
http://dx.doi.org/10.1155/2013/504076
Research Article

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

1Department of Mathematics, China Jiliang University, Hangzhou 310018, China
2Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China

Received 27 September 2013; Accepted 21 October 2013

Academic Editor: Antonio M. Peralta

Copyright © 2013 XianFa Luo and JianYong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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