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A functional equation involving iterates of a bijection on the unit interval. II. (English) Zbl 0899.39005
An example is exhibited of a functional equation of the form $\sum^n_{k=0} c_kf^k (x)=0$ $$(c_k\in \mathbb{R}$$, $$\sum^n_{k=0} c_k=0$$, $$f^k$$ denoting the $$k$$-th iterate of $$f)$$ which has a bijective solution $$f$$ (of $$[0,1]$$ onto itself) and such that $$f^r(x)\neq x$$ for any $$r>0$$. Thus the problem posed by the authors in part I [ibid. No. 7, 899-908 (1993; Zbl 0518.39005)] has been settled.

##### MSC:
 39B12 Iteration theory, iterative and composite equations
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##### References:
 [1] Mukherjea, A.; Ratti, J.S., On a functional equation involving iterates of a bijection on the unit interval, Nonlinear analysis: theory, methods & applications, 7, 8, 899-908, (1983) · Zbl 0518.39005 [2] Ratti, J.S.; Lin, Y.F., A functional equation involving f and f−1, Colloquium mathematicum, LX/LXI, 519-523, (1990) · Zbl 0731.39006 [3] Weinian Zhang, The discussion on the iterated equation σi = 1naifi(x) = F(x), (1985), Inst. of Math. Sciences, Academia Sinica China
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