Functions of bounded variation arising from a generalized two-normed space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913810091081728 |
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| author | Ferrer, Osmin Ferrer, Kandy Cure, Jaffeth |
| author_facet | Ferrer, Osmin Ferrer, Kandy Cure, Jaffeth |
| contents | The first formal development of functions with bounded variation in normed spaces is attributed to Chistyakov [5], and was later extended to the context of 2-normed spaces by Cure, Ferrer S., and Ferrer V. [6]. In this paper, we elaborate on this extension (Definition 4.5), exploring its fundamental properties. The foundational characteristics of functions of bounded 2-variation within the context of generalized two-normed spaces are explored in detail (see Theorems 4.4, 4.12, 4.13). Additionally, it is shown that a function of bounded variation defined on a semi-normed space can generate a function of bounded 2-variation in the context of generalized two-normed spaces (Proposition 4.10). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functions of bounded variation arising from a generalized two-normed space Ferrer, Osmin Ferrer, Kandy Cure, Jaffeth Functional Analysis 46C50, 46C05, 26A45 The first formal development of functions with bounded variation in normed spaces is attributed to Chistyakov [5], and was later extended to the context of 2-normed spaces by Cure, Ferrer S., and Ferrer V. [6]. In this paper, we elaborate on this extension (Definition 4.5), exploring its fundamental properties. The foundational characteristics of functions of bounded 2-variation within the context of generalized two-normed spaces are explored in detail (see Theorems 4.4, 4.12, 4.13). Additionally, it is shown that a function of bounded variation defined on a semi-normed space can generate a function of bounded 2-variation in the context of generalized two-normed spaces (Proposition 4.10). |
| title | Functions of bounded variation arising from a generalized two-normed space |
| topic | Functional Analysis 46C50, 46C05, 26A45 |
| url | https://arxiv.org/abs/2504.19068 |