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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:
39B12Iterative and composite functional equations
39B32Functional equations for complex functions
39B82Stability, separation, extension, and related topics
37E05Maps of the interval (piecewise continuous, continuous, smooth)
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