Geodesic
Biconnected Multifunctions of Trees which have an end Point as Fixed Point or Coincidence
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 461-467

Voir la notice de l'article provenant de la source Cambridge University Press

It was proved almost forty years ago that every mapping of a tree into itself has at least one fixed point, but not much is known so far about the structure of the possible fixed point sets. One topic related to this question, the study of homeomorphisms and monotone mappings of trees which leave an end point fixed, was first considered by G. E. Schweigert [6] and continued by L. E. Ward, Jr. [8] and others. One result by Schweigert and Ward is the following: any monotone mapping of a tree onto itself which leaves an end point fixed, also leaves at least one other point fixed.It is further known that not only single-valued mappings, but also upper semi-continuous (use) and connected-valued multifunctions of trees have a fixed point [7], and that two use and biconnected multifunctions from one tree onto another have a coincidence [5]. 
Schirmer, Helga. Biconnected Multifunctions of Trees which have an end Point as Fixed Point or Coincidence. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 461-467. doi: 10.4153/CJM-1971-049-6
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