The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-24
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
Let C be a closed bounded convex subset of a real Banach space X with 0 as its interior and pC the Minkowski functional generated by the set C.
For a nonempty set G in X and x∈X, g0∈G is called the generalized best approximation to x from G if pC(g0−x)≤pC(g−x) for all g∈G.
In this paper, we will give a distance formula under pC 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.
American Psychological Association (APA)
Luo, Xianfa& Wang, JianYong. 2013. The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-476843
Modern Language Association (MLA)
Luo, Xianfa& Wang, JianYong. The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces. Abstract and Applied Analysis No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-476843
American Medical Association (AMA)
Luo, Xianfa& Wang, JianYong. The Representation and Continuity of a Generalized Metric Projection onto a Closed Hyperplane in Banach Spaces. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-476843
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-476843