2-Strict Convexity and Continuity of Set-Valued Metric Generalized Inverse in Banach Spaces. (18th December 2013)

• 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: 2013-12-18
• 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, if X is approximately compact and X is 2-strictly convex, then metric generalized inverses of bounded linear operators in X 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 mapping T ∂ to be continuous mapping is given.