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...

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Detalles Bibliográficos
Autores: Ferrera Cuesta, Juan, Gómez Gil, Javier, Llorente Jorge, Jesús
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/133207
Acceso en línea:https://hdl.handle.net/20.500.14352/133207
Access Level:acceso abierto
Palabra clave:The Takagi function
Generalized Takagi class
Nowhere differentiable functions
Fréchet subdifferential
Análisis matemático
1202.10 Funciones de Variables Reales
1202.17 Medida, Integración, Area
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spelling A characterization of the nowhere differentiable functions in the Generalized Takagi classFerrera Cuesta, JuanGómez Gil, JavierLlorente Jorge, JesúsThe Takagi functionGeneralized Takagi classNowhere differentiable functionsFréchet subdifferentialAnálisis matemático1202.10 Funciones de Variables Reales1202.17 Medida, Integración, AreaIn 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].Springer NatureUniversidad Complutense de Madrid20242024-01-0120242024-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/133207reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1332072026-06-02T12:44:21Z
dc.title.none.fl_str_mv A characterization of the nowhere differentiable functions in the Generalized Takagi class
title A characterization of the nowhere differentiable functions in the Generalized Takagi class
spellingShingle A characterization of the nowhere differentiable functions in the Generalized Takagi class
Ferrera Cuesta, Juan
The Takagi function
Generalized Takagi class
Nowhere differentiable functions
Fréchet subdifferential
Análisis matemático
1202.10 Funciones de Variables Reales
1202.17 Medida, Integración, Area
title_short A characterization of the nowhere differentiable functions in the Generalized Takagi class
title_full A characterization of the nowhere differentiable functions in the Generalized Takagi class
title_fullStr A characterization of the nowhere differentiable functions in the Generalized Takagi class
title_full_unstemmed A characterization of the nowhere differentiable functions in the Generalized Takagi class
title_sort A characterization of the nowhere differentiable functions in the Generalized Takagi class
dc.creator.none.fl_str_mv Ferrera Cuesta, Juan
Gómez Gil, Javier
Llorente Jorge, Jesús
author Ferrera Cuesta, Juan
author_facet Ferrera Cuesta, Juan
Gómez Gil, Javier
Llorente Jorge, Jesús
author_role author
author2 Gómez Gil, Javier
Llorente Jorge, Jesús
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv The Takagi function
Generalized Takagi class
Nowhere differentiable functions
Fréchet subdifferential
Análisis matemático
1202.10 Funciones de Variables Reales
1202.17 Medida, Integración, Area
topic The Takagi function
Generalized Takagi class
Nowhere differentiable functions
Fréchet subdifferential
Análisis matemático
1202.10 Funciones de Variables Reales
1202.17 Medida, Integración, Area
description 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].
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-01
2024
2024-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/133207
url https://hdl.handle.net/20.500.14352/133207
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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