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

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## 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.## References

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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
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 2531-2538 - MSC (2020): Primary 46B20, 46B50, 47H10
- DOI: https://doi.org/10.1090/proc/15393
- MathSciNet review: 4246803