Jungck theorem for triangular maps and related results

Authors

  • M. Grinc Silesian University
  • L. Snoha Matej Bel University

DOI:

https://doi.org/10.4995/agt.2000.3025

Keywords:

Compatible maps, Complete invariance property, Jungck theorem, Jachymski theorem, Fixed point

Abstract

We prove that a continuous triangular map G of the n-dimensional cube In has only fixed points and no other periodic points if and only if G has a common fixed point with every continuous triangular map F that is nontrivially compatible with G. This is an analog of Jungck theorem for maps of a real compact interval. We also discuss possible extensions of Jungck theorem, Jachymski theorem and some related results to more general spaces. In particular, the spaces with the fixed point property and the complete invariance property are considered.

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Author Biographies

M. Grinc, Silesian University

Institute of Mathematics

L. Snoha, Matej Bel University

Departament of Mathematics

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Published

2000-10-01

How to Cite

[1]
M. Grinc and L. Snoha, “Jungck theorem for triangular maps and related results”, Appl. Gen. Topol., vol. 1, no. 1, pp. 83–92, Oct. 2000.

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Articles