×

Jungck theorem for triangular maps and related results. (English) Zbl 0991.54046

It is proved that a continuous triangular map \(G\) of the \(n\)-dimensional cube \(I^n\) 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 \(G\). The maps are compatible if they commute on the set of their coincidence points. The compatible maps are nontrivially compatible if the set of their coincidence points is nonempty. This is an analogue of Jungck theorem for maps of a real compact interval.

MSC:

54H20 Topological dynamics (MSC2010)
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI