Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 504076, 6 pages.
The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces
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.
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 504076, 6 pages.
First available in Project Euclid: 26 February 2014
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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