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A general class of iterative equations on the unit circle

Marek Cezary Zdun; Wei Nian Zhang — 2007

Czechoslovak Mathematical Journal

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.

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