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- Title
On regularity for de Rham's functional equations.
- Authors
Okamura, Kazuki
- Abstract
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions making up the equation, we improve some results in Hata (Japan J Appl Math 2:381-414, 1985). Our results are applicable to some cases when the functions making up the equation are non-linear functions on an interval, specifically, polynomials and linear fractional transformations. Our results imply the singularity of some well-known singular functions, in particular, Minkowski's question-mark function, and, some small perturbed functions of the singular functions.
- Subjects
FUNCTIONAL equations; METRIC spaces; POLYNOMIALS; LINEAR equations; MINKOWSKI space
- Publication
Aequationes Mathematicae, 2016, Vol 90, Issue 6, p1071
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-016-0439-6