2-Strict Convexity and Continuity of Set-Valued Metric Generalized Inverse in Banach Spaces

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 $T^{\partial }$ to be continuous mapping is given.