A general class of iterative equations on the unit circle

Marek Cezary Zdun; Wei Nian Zhang

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 809-829
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Zdun, Marek Cezary, and Zhang, Wei Nian. "A general class of iterative equations on the unit circle." Czechoslovak Mathematical Journal 57.3 (2007): 809-829. <http://eudml.org/doc/31164>.

@article{Zdun2007,
abstract = {A class of functional equations with nonlinear iterates is discussed on the unit circle $\{\mathbb \{T\}\}^1$. By lifting maps on $\{\mathbb \{T\}\}^1$ and maps on the torus $\{\mathbb \{T\}\}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.},
author = {Zdun, Marek Cezary, Zhang, Wei Nian},
journal = {Czechoslovak Mathematical Journal},
keywords = {iterative equation; circle; lift; orientation-preserving; continuation; iterative equation; circle; lift; orientation-preserving; continuation},
language = {eng},
number = {3},
pages = {809-829},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A general class of iterative equations on the unit circle},
url = {http://eudml.org/doc/31164},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Zdun, Marek Cezary
AU - Zhang, Wei Nian
TI - A general class of iterative equations on the unit circle
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 809
EP - 829
AB - A class of functional equations with nonlinear iterates is discussed on the unit circle ${\mathbb {T}}^1$. By lifting maps on ${\mathbb {T}}^1$ and maps on the torus ${\mathbb {T}}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
LA - eng
KW - iterative equation; circle; lift; orientation-preserving; continuation; iterative equation; circle; lift; orientation-preserving; continuation
UR - http://eudml.org/doc/31164
ER -

References

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