A geometric construction of continuous, strictly increasing singular functions

DOI10.3792/PJAA.83.114zbMath1163.26303OpenAlexW2165408496MaRDI QIDQ935587

Hisashi Okamoto, Marcus Wunsch

Publication date: 11 August 2008

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1200672011

zbMATH Keywords

continuoussingular functionsmonotonically increasing function

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15)

Related Items (15)

Singular function emerging from one-dimensional elementary cellular automaton rule 150 ⋮ The infinite derivatives of Okamoto's self-affine functions: an application of \(\beta\)-expansions ⋮ A singular function with a non-zero finite derivative on a dense set ⋮ Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds ⋮ A study of topological conjugacies between alternate representation systems ⋮ Local convergence of Newton's method under majorant condition ⋮ The partial derivative of Okamoto's functions with respect to the parameter ⋮ Singular distribution functions for random variables with stationary digits ⋮ A singular function with a non-zero finite derivative ⋮ A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic ⋮ Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition ⋮ The Minkowski question mark function: explicit series for the dyadic period function and moments ⋮ On regularity for de Rham's functional equations ⋮ On the critical case of Okamoto's continuous non-differentiable functions ⋮ Distribution of Values of Cantor Type Fractal Functions with Specified Restrictions

Cites Work

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• A remark on continuous, nowhere differentiable functions
• Riesz--Nágy singular functions revisited
• On the critical case of Okamoto's continuous non-differentiable functions
• An extension of Minkowski's singular function
• Simple constructions of nowhere differentiable continuous functions
• An Increasing Continuous Singular Function
• On Some Singular Monotonic Functions Which Are Strictly Increasing

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