Bipolar Theorem and Some of Its Applications in Fuzzy Quasi-Normed Space

Jianrong Wu, Lei Hua and Zhenyu Jin

Journal of Mathematics, 2025, vol. 2025, 1-8

Abstract: The classical bipolar theorem plays an important role in functional analysis. This paper generalizes this theorem to fuzzy quasi-normed spaces, which include asymmetric normed space and fuzzy normed space as special cases. First, the concept of the asymmetric polar of a subset is introduced in the fuzzy quasi-normed space, its basic properties, such as closedness and compactness, are investigated. After the notion of asymmetric bipolar being proposed, the bipolar theorem is established. Additionally, some conclusions are presented based on the bipolar theorem. For example, a necessary and sufficient condition for the linear hull of a subset to be dense is given, a representation of the gauge of a subset is presented, and a characteristic of the family of equicontinuous linear functional is proved. These results generalize the existing results.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2025/9142011.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2025/9142011.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9142011

DOI: 10.1155/jom/9142011

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().