A characterization of the nowhere differentiable functions in the Generalized Takagi class

被引：0
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作者：
Ferrera, Juan [1 ]
Gómez Gil, Javier [2 ]
Llorente, Jesús [1 ]
机构：
[1] IMI, Departamento de Análisis Matemático y Matemática Aplicada, Facultad Ciencias Matemáticas, Universidad Complutense, Madrid,28040, Spain
[2] Departamento de Análisis Matemático y Matemática Aplicada, Facultad Ciencias Matemáticas, Universidad Complutense, Madrid,28040, Spain
来源：
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas | 2025年 / 119卷 / 01期
关键词：
The Takagi function; Generalized Takagi class; Nowhere differentiable functions; Fréchet subdifferential; Primary 26A27; 26A30; 26A24;
D O I：
10.1007/s13398-024-01673-1
中图分类号：
学科分类号：
摘要：
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 c0. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2024.
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