Some results for conjugate equations
arXiv:1806.06197 · doi:10.1007/s00010-018-0633-9
Abstract
In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider regularity of solutions. In our framework, two iterated function systems are associated with a series of conjugate equations. We state local regularity by using the invariant measures of the two iterated function systems with a common probability vector. We give several examples, especially an example such that infinitely many solutions exists, and a new class of fractal functions on the two-dimensional standard Sierpinski gasket which are not harmonic functions or fractal interpolation functions. We also consider a certain kind of stability.
28 pages; to appear in Aequationes mathematicae
References in corpus (5)
- Fractal analysis for sets of non-differentiability of Minkowski's question mark function
- On weakly hyperbolic iterated functions systems
- On regularity for de Rham's functional equations
- Singularity results for functional equations driven by linear fractional transformations
- Invariant measures of Markov operators associated to iterated function systems consisting of phi-max-contractions with probabilities