Set-Valued Fractal Approximation for Countable Data Sets
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914050082865152 |
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| author | Kaur, Parneet Lal, Rattan Kumar, Ankit Verma, Saurabh |
| author_facet | Kaur, Parneet Lal, Rattan Kumar, Ankit Verma, Saurabh |
| contents | Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We first provide a construction of fractal functions for countable data sets and use these functions in the approximation and study of set-valued mappings. We also show the existence and uniqueness of an invariant Borel measure supported on the graph of a set-valued fractal function. In addition, we obtain some effective bounds on the dimensions of the constructed set-valued fractal functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Set-Valued Fractal Approximation for Countable Data Sets Kaur, Parneet Lal, Rattan Kumar, Ankit Verma, Saurabh Functional Analysis 28A80 Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We first provide a construction of fractal functions for countable data sets and use these functions in the approximation and study of set-valued mappings. We also show the existence and uniqueness of an invariant Borel measure supported on the graph of a set-valued fractal function. In addition, we obtain some effective bounds on the dimensions of the constructed set-valued fractal functions. |
| title | Set-Valued Fractal Approximation for Countable Data Sets |
| topic | Functional Analysis 28A80 |
| url | https://arxiv.org/abs/2504.08491 |