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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2605.00047 |
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| _version_ | 1866909006651457536 |
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| author | Jiménez-Fernández, Eduardo Rodríguez-López, Jesús Sánchez-Martín-Orozco, Aurora Sánchez-Pérez, Enrique A. |
| author_facet | Jiménez-Fernández, Eduardo Rodríguez-López, Jesús Sánchez-Martín-Orozco, Aurora Sánchez-Pérez, Enrique A. |
| contents | In the paper [E. Jiménez-Fernández, J. Rodr\'ıguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space $(\mathbb{R},M_{ϕ,g},\ast).$ However, while the function $ϕ$ is only required to be increasing, some results of the paper implicitly assume that $ϕ$ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires $ϕ$ to be also left-continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps Jiménez-Fernández, Eduardo Rodríguez-López, Jesús Sánchez-Martín-Orozco, Aurora Sánchez-Pérez, Enrique A. General Mathematics 26A16, 54E70, 54C20 In the paper [E. Jiménez-Fernández, J. Rodr\'ıguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space $(\mathbb{R},M_{ϕ,g},\ast).$ However, while the function $ϕ$ is only required to be increasing, some results of the paper implicitly assume that $ϕ$ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires $ϕ$ to be also left-continuous. |
| title | A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps |
| topic | General Mathematics 26A16, 54E70, 54C20 |
| url | https://arxiv.org/abs/2605.00047 |