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Convexification of super weakly compact sets and measure of super weak noncompactness


Author: Kun Tu
Journal: Proc. Amer. Math. Soc. 149 (2021), 2531-2538
MSC (2020): Primary 46B20, 46B50, 47H10
DOI: https://doi.org/10.1090/proc/15393
Published electronically: March 22, 2021
MathSciNet review: 4246803
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Abstract | References | Similar Articles | Additional Information

Abstract: In the paper, we give a quantitative version of the positive answer to the open question about the convex hull of a super weakly compact set. Measure of super weak noncompactness $\sigma$ is introduced and proved to share several nice properties with the Hausdorff measure of noncompactness. As an application, a fixed point theorem for $\sigma$-condensing maps is given.


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Additional Information

Kun Tu
Affiliation: School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, People’s Republic of China
Address at time of publication: School of Mathematical Sciences, Yangzhou University, Siwangting Road No.180, Yangzhou 225002, People’s Republic of China
MR Author ID: 1107434
ORCID: 0000-0002-6197-0372
Email: tukun@yzu.edu.cn

Received by editor(s): May 11, 2020
Received by editor(s) in revised form: September 17, 2020
Published electronically: March 22, 2021
Additional Notes: The author was partially supported by NSFC, grant no. 11701501, and the post doctoral funding of Yangzhou University, grant no. 137070608.
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2021 American Mathematical Society