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

Shaoqiang Shang and Yunan Cui

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/384639

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:384639

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