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 |
| Summary: | 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. |
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| ISSN: | 0120-419X 2145-8472 |