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August 2016 Near dentability and continuity of the set-valued metric generalized inverse in Banach spaces
Shaoqiang Shang
Ann. Funct. Anal. 7(3): 508-520 (August 2016). DOI: 10.1215/20088752-3625003

Abstract

In this paper, upper semicontinuity and continuity of the set-valued metric generalized inverse T in nearly dentable spaces are investigated using the methods of Banach space geometry. Moreover, it is proved that if X is a nearly dentable space and if C is a closed convex set of X, then C is approximatively compact if and only if PC(x) is compact for any xX.

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Shaoqiang Shang. "Near dentability and continuity of the set-valued metric generalized inverse in Banach spaces." Ann. Funct. Anal. 7 (3) 508 - 520, August 2016. https://doi.org/10.1215/20088752-3625003

Information

Received: 4 November 2015; Accepted: 27 February 2016; Published: August 2016
First available in Project Euclid: 22 August 2016

zbMATH: 06621456
MathSciNet: MR3540448
Digital Object Identifier: 10.1215/20088752-3625003

Subjects:
Primary: 46B20

Keywords: approximative compactness , nearly dentable space , set-valued metric generalized inverse , upper semicontinuity

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.7 • No. 3 • August 2016
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