A characterization of the nowhere differentiable functions in the Generalized Takagi class
In this paper, we explore the non-differentiability behavior of the functions belonging to the Generalized Takagi class, a recent generalization of the Takagi function. It is derived by replacing the dyadic numbers used in the definition of classical Takagi function with an arbitrary countable and d...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/133207 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/133207 |
| Access Level: | acceso abierto |
| Palavra-chave: | The Takagi function Generalized Takagi class Nowhere differentiable functions Fréchet subdifferential Análisis matemático 1202.10 Funciones de Variables Reales 1202.17 Medida, Integración, Area |
| Resumo: | In this paper, we explore the non-differentiability behavior of the functions belonging to the Generalized Takagi class, a recent generalization of the Takagi function. It is derived by replacing the dyadic numbers used in the definition of classical Takagi function with an arbitrary countable and dense subset of [0, 1]. Subject to specific conditions on the decomposition of such a set, we demonstrate that a function within this class is nowhere differentiable if and only if the sequence of weights does not belong to c[subíndice 0]. |
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