Fractal negations. (English) Zbl 0834.26007
The authors establish the fractal nature and find the corresponding iterated (affine) function systems for graphs of singular continuous functions \(F : [0,1] \to [0,1]\). In particular, they consider the de Rham function, strong negations (nonincreasing functions satisfying \(F(F(x)) \equiv x)\) and \(k\)-negations (strong negations satisfying also \(F(kx) \equiv (1 - k) F(x) + k\) for some \(0 < k < 1)\).
Reviewer: I.S.Molchanov (Glasgow)
MSC:
26A30 | Singular functions, Cantor functions, functions with other special properties |
28A80 | Fractals |