2-Strict Convexity and Continuity of Set-Valued Metric Generalized Inverse in Banach Spaces. (18th December 2013) - Shang, Shaoqiang; Cui, Yunan
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.