Nemytskii operator on generalized bounded variation space
In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f (t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R. To cite...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
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Universidad Industrial de Santander
2014-05-01
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| Series: | Revista Integración |
| Subjects: | |
| Online Access: | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064 |
| _version_ | 1828813832597798912 |
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| author | René Erlín Castillo Humberto Rafeiro Eduard Trousselot |
| author_facet | René Erlín Castillo Humberto Rafeiro Eduard Trousselot |
| author_sort | René Erlín Castillo |
| collection | DOAJ |
| description | In this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f (t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R.
To cite this article: R. E. Castillo, H. Rafeiro, E. Trousselot, Nemytskii operator on generalized bounded variation space, Rev. Integr. Temas Mat. 32 (2014), no. 1, 71–90. |
| first_indexed | 2024-12-12T10:11:00Z |
| format | Article |
| id | doaj.art-3de9ef110914411b9458d2ebb2a0cd60 |
| institution | Directory Open Access Journal |
| issn | 0120-419X 2145-8472 |
| language | Spanish |
| last_indexed | 2024-12-12T10:11:00Z |
| publishDate | 2014-05-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista Integración |
| spelling | doaj.art-3de9ef110914411b9458d2ebb2a0cd602022-12-22T00:27:48ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722014-05-01321Nemytskii operator on generalized bounded variation spaceRené Erlín Castillo0Humberto Rafeiro1Eduard Trousselot2Universidad Nacional de ColombiaPontificia Universidad JaverianaUniversidad de OrienteIn this paper we show that if the Nemytskii operator maps the (φ, α)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the (φ, α)-bounded variation space such that f (t, y) = g(t)y + h(t) for all t ∈ [a, b], y ∈ R. To cite this article: R. E. Castillo, H. Rafeiro, E. Trousselot, Nemytskii operator on generalized bounded variation space, Rev. Integr. Temas Mat. 32 (2014), no. 1, 71–90.https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064Riesz p-variation(φ, α)-bounded variation |
| spellingShingle | René Erlín Castillo Humberto Rafeiro Eduard Trousselot Nemytskii operator on generalized bounded variation space Revista Integración Riesz p-variation (φ, α)-bounded variation |
| title | Nemytskii operator on generalized bounded variation space |
| title_full | Nemytskii operator on generalized bounded variation space |
| title_fullStr | Nemytskii operator on generalized bounded variation space |
| title_full_unstemmed | Nemytskii operator on generalized bounded variation space |
| title_short | Nemytskii operator on generalized bounded variation space |
| title_sort | nemytskii operator on generalized bounded variation space |
| topic | Riesz p-variation (φ, α)-bounded variation |
| url | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064 |
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