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
