Displaying similar documents to “Strictly decreasing solutions of a class of iterative equations on the unit circle.”

A general class of iterative equations on the unit circle

Marek Cezary Zdun, Wei Nian Zhang (2007)

Czechoslovak Mathematical Journal

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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.

Open maps between Knaster continua

Carl Eberhart, J. Fugate, Shannon Schumann (1999)

Fundamenta Mathematicae

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We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.