Distance Distribution Functions and Probabilistic Metric Spaces on C*-algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909798453215232 |
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| author | Abazari, Rasoul |
| author_facet | Abazari, Rasoul |
| contents | In this paper, by using the concept of positive elements of $C^*$-algebras instead of the real numbers $\mathbb{R}$, a generalization of distribution functions, with a particular focus on distance distribution functions has been introduced as a novel approach in statistical mathematics. Also, by applying this concept, probabilistic metric space on $C^*$-algebras is defined and some properties such as topology and fixed point theorems have been investigated. Finally, some examples and applications to integral equations are given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distance Distribution Functions and Probabilistic Metric Spaces on C*-algebras Abazari, Rasoul Operator Algebras Functional Analysis 54E70, 47H10, 46L05 In this paper, by using the concept of positive elements of $C^*$-algebras instead of the real numbers $\mathbb{R}$, a generalization of distribution functions, with a particular focus on distance distribution functions has been introduced as a novel approach in statistical mathematics. Also, by applying this concept, probabilistic metric space on $C^*$-algebras is defined and some properties such as topology and fixed point theorems have been investigated. Finally, some examples and applications to integral equations are given. |
| title | Distance Distribution Functions and Probabilistic Metric Spaces on C*-algebras |
| topic | Operator Algebras Functional Analysis 54E70, 47H10, 46L05 |
| url | https://arxiv.org/abs/2509.16498 |