Open AccessJungck theorem for triangular maps and related results
Author(s) -
M. Grinc,
Ľubomír Snoha
Publication year - 2000
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2000.3025
Subject(s) - mathematics , cube (algebra) , fixed point theorem , fixed point , interval (graph theory) , discrete mathematics , property (philosophy) , point (geometry) , fixed point property , combinatorics , pure mathematics , mathematical analysis , geometry , philosophy , epistemology
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