Second order differentiability and related topics in the Takagi Class
In this paper we study some properties concerning the second order differentiability of the functions belonging to the Takagi class as well as the size of the sets where these properties hold. In particular, we characterize the set of points where these functions have a Taylor expansion of order two...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/133275 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/133275 |
| Access Level: | acceso abierto |
| Palabra clave: | Takagi class Second order differentiability Taylor expansion of order two Stepanov condition of order two Convexity Análisis matemático 1202.06 Convexidad, desigualdades 1202.10 Funciones de Variables Reales 1202.17 Medida, Integración, Area |
| Sumario: | In this paper we study some properties concerning the second order differentiability of the functions belonging to the Takagi class as well as the size of the sets where these properties hold. In particular, we characterize the set of points where these functions have a Taylor expansion of order two. Moreover, we also characterize when they satisfy a Stepanov condition of order two at a point. In this context, the convexity of such functions is also investigated. Finally, some interesting examples are provided. |
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