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