AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (240.6 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

The index of strong rotundity

Department of Mathematics, College of Engineering, University of Cadiz, Avda. de la Universidad 10, Puerto Real 11519, Spain
Show Author Information

Abstract

The index of strong rotundity is introduced. This index is used to determine how far an element of the unit sphere of a real Banach space is from being a strongly exposed point of the unit ball. This index is computed for Hilbert spaces. Characterizations of the set of rotund points and the set of smooth points are provided for a better understanding of the construction of the index of strong rotundity. Finally, applications to the stereographic projection are provided.

Keywords

exposed pointrotund pointsmooth pointBanach spaceHilbert space
CLC number: 46B20

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20477-20486
DOI: 10.3934/math.20231043

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
García-Pacheco FJ. The index of strong rotundity. AIMS Mathematics, 2023, 8(9): 20477-20486. https://doi.org/10.3934/math.20231043

3

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 02 March 2023
Revised: 08 June 2023
Accepted: 13 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)