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2014 2-Strict Convexity and Continuity of Set-Valued Metric Generalized Inverse in Banach Spaces
Shaoqiang Shang, Yunan Cui
Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/384639

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.

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Shaoqiang Shang. Yunan Cui. "2-Strict Convexity and Continuity of Set-Valued Metric Generalized Inverse in Banach Spaces." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/384639

Information

Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07022278
MathSciNet: MR3166606
Digital Object Identifier: 10.1155/2014/384639

Rights: Copyright © 2014 Hindawi

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