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A general class of iterative equations on the unit circle. (English) Zbl 1174.39005
Summary: A class of functional equations with nonlinear iterates is discussed on the unit circle ${𝕋}^{1}$. By lifting maps on ${𝕋}^{1}$ and maps on the torus ${𝕋}^{n}$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
MSC:
 39B12 Iterative and composite functional equations 39B32 Functional equations for complex functions 39B82 Stability, separation, extension, and related topics 37E05 Maps of the interval (piecewise continuous, continuous, smooth)
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