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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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