On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915961684099072 |
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| author | Benavente, Ana Ponce, Juan Costa Favier, Sergio |
| author_facet | Benavente, Ana Ponce, Juan Costa Favier, Sergio |
| contents | Given an approximately continuous function $f$ in an Orlicz space $L^Φ([a,b]),$ for a suitable class of convex functions $Φ,$ we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in $L^Φ([a,b]).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces Benavente, Ana Ponce, Juan Costa Favier, Sergio Functional Analysis Given an approximately continuous function $f$ in an Orlicz space $L^Φ([a,b]),$ for a suitable class of convex functions $Φ,$ we employ a characterization of the best monotone approximation set to establish its continuity, which in turn yields the uniqueness property for the best monotone approximation in $L^Φ([a,b]).$ |
| title | On the Uniqueness of Best Non-decreasing Approximation in Orlicz Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.09210 |