Approximate differentiability in the generalized Takagi-van der Waerden class

DOI10.1007/s10476-022-0135-9OpenAlexW4223522026MaRDI QIDQ2678406

Jesús Llorente, Javier Gómez Gil, Juan Ferrera

Publication date: 23 January 2023

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10476-022-0135-9

zbMATH Keywords

Hölder continuityLipschitz propertyapproximate differentiabilityLusin-type propertygeneralized Takagi-van der Waerden class

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Singular functions, Cantor functions, functions with other special properties (26A30) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Cites Work

• The Takagi function: a survey
• On generalized Takagi functions
• On the Hölder continuity of certain functions
• Approximate Taylor polynomials and differentiation of functions
• Subdifferentiable functions satisfy Lusin properties of class \(C^1\) or \(C^2\)
• Differentiability of the functions of the generalized Takagi class
• Second order differentiability and related topics in the Takagi class
• Superdifferential analysis of the Takagi-van der Waerden functions
• On the level sets of the Takagi-van der Waerden functions
• Infinite derivatives of the Takagi-Van der Waerden functions
• The Takagi function and its generalization
• The Takagi Function and Its Properties
• Non approximate derivability of the Takagi function

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