2-Strict Convexity and Continuity of Set-Valued Metric Generalized Inverse in Banach Spaces. (2nd January 2014)

• Record Type: Journal Article
• Authors: Shang, Shaoqiang; Cui, Yunan
• Other Names: Donatelli Marco Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-01-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/384639
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Authors investigate the metric generalized inverses of linear operators in Banach spaces. Authors prove by the methods of geometry of Banach spaces that, ifX is approximately compact andX is 2-strictly convex, then metric generalized inverses of bounded linear operators inX are upper semicontinuous. Moreover, authors also give criteria for metric generalized inverses of bounded linear operators to be lower semicontinuous. Finally, a sufficient condition for set-valued mappingT ∂ to be continuous mapping is given.