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On linear homogeneous functional equations in the indeterminate case. (English) Zbl 0555.39003
It is shown that in the case where $$| g(\xi)| =1$$ almost all equations of the form $$\phi (f(x))=g(x)\phi (x)$$, $$x\in I\subset {\mathbb{R}}$$, $$\xi\in I$$ (all in the sense of Baire category) have exactly one continuous solution $$\phi$$ : $$I\to {\mathbb{R}}$$ (the zero function). Here I is a compact interval, f,g: $$I\to {\mathbb{R}}$$ are continuous, g(x)$$\neq 0$$ in I, and $$0<(f(x)-\xi)/(x-\xi)<1$$ for $$x\in I\setminus \{\xi \}$$.
Reviewer: B.Choczewski

##### MSC:
 39B12 Iteration theory, iterative and composite equations
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