Continuous Nowhere-Differentiable Functions--an Application of Contraction Mappings

DOI10.2307/2323856zbMath0752.26005OpenAlexW2004250109MaRDI QIDQ3983926

Hidefumi Katsuura

Publication date: 27 June 1992

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2323856

zbMATH Keywords

fixed pointBanach contraction principlenowhere-differentiable functions

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

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Computational aspects of Kolmogorov's superposition theorem ⋮ The infinite derivatives of Okamoto's self-affine functions: an application of \(\beta\)-expansions ⋮ Non-differentiability and Hölder properties of self-affine functions ⋮ Functional equations for peculiar functions ⋮ The pointwise Hölder spectrum of general self-affine functions on an interval ⋮ Differentiability of a two-parameter family of self-affine functions ⋮ Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions ⋮ The partial derivative of Okamoto's functions with respect to the parameter ⋮ Some types of numeral systems and their modeling ⋮ Differentiability and Hölder spectra of a class of self-affine functions ⋮ Self-affine fractal functions and wavelet series ⋮ A probabilistic property of Katsuura's continuous nowhere differentiable function ⋮ Certain singular distributions and fractals ⋮ The Nonexistence of a Continuous Surjection from a Continuum onto its Square ⋮ Note on a chaotic map that generates nowhere-differentiability

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