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....
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
| Published: |
Universidad Industrial de Santander
2014-06-01
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| Series: | Revista Integración |
| Subjects: | |
| Online Access: | http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064/4410 |
| _version_ | 1819292513312178176 |
|---|---|
| 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.
Resumen. En este artículo demostramos que si el operador de Nemytskii lleva
el espacio de variación (φ, α)-acotada en sí mismo, y satisface cierta condición
de Lipschitz, entonces existen dos funciones g y h perteneciendo al espacio
de variación (φ, α)-acotada tal que f(t, y) = g(t)y + h(t) para todo t ∈ [a, b],
y ∈ R. |
| first_indexed | 2024-12-24T03:55:43Z |
| format | Article |
| id | doaj.art-4d998173c1284934a3ad13a3d9a43d70 |
| institution | Directory Open Access Journal |
| issn | 0120-419X 2145-8472 |
| language | Spanish |
| last_indexed | 2024-12-24T03:55:43Z |
| publishDate | 2014-06-01 |
| publisher | Universidad Industrial de Santander |
| record_format | Article |
| series | Revista Integración |
| spelling | doaj.art-4d998173c1284934a3ad13a3d9a43d702022-12-21T17:16:26ZspaUniversidad Industrial de SantanderRevista Integración0120-419X2145-84722014-06-013217190Nemytskii 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. Resumen. En este artículo demostramos que si el operador de Nemytskii lleva el espacio de variación (φ, α)-acotada en sí mismo, y satisface cierta condición de Lipschitz, entonces existen dos funciones g y h perteneciendo al espacio de variación (φ, α)-acotada tal que f(t, y) = g(t)y + h(t) para todo t ∈ [a, b], y ∈ R.http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064/4410Riesz p-variationα)-bounded variationp-variación de Riesz |
| spellingShingle | René Erlín Castillo Humberto Rafeiro Eduard Trousselot Nemytskii operator on generalized bounded variation space Revista Integración Riesz p-variation α)-bounded variation p-variación de Riesz |
| 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 α)-bounded variation p-variación de Riesz |
| url | http://revistas.uis.edu.co/index.php/revistaintegracion/article/view/4064/4410 |
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