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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 \(0 < k < 1)\).

MSC:

26A30 Singular functions, Cantor functions, functions with other special properties
28A80 Fractals