Functional equations connected with peculiar curves. (English) Zbl 0615.58017
Iteration theory and its functional equations, Proc. Int. Symp., Schloß Hofen (Lochau)/Austria 1984, Lect. Notes Math. 1163, 33-40 (1985).
[For the entire collection see Zbl 0587.00008.]
The author indicates how Bajraktarevic’s functional equation, \(x(t)=f(t,x(b(t)))\), can be used in order to recover many classical nondifferentiable functions, as these from Weierstrass, Knopp, van der Waerden, Hildebrandt and Sierpinski. More recent curves and new ones can be generated also. An iterative scheme for the graphical computation of the curves related to this functional equation is given at the end. There are six graphical representations with associated numerical data.
The author indicates how Bajraktarevic’s functional equation, \(x(t)=f(t,x(b(t)))\), can be used in order to recover many classical nondifferentiable functions, as these from Weierstrass, Knopp, van der Waerden, Hildebrandt and Sierpinski. More recent curves and new ones can be generated also. An iterative scheme for the graphical computation of the curves related to this functional equation is given at the end. There are six graphical representations with associated numerical data.
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 39B12 | Iteration theory, iterative and composite equations |
| 26A27 | Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives |
