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Biconnected Multifunctions of Trees which have an end Point as Fixed Point or Coincidence

Published online by Cambridge University Press:  20 November 2018

Helga Schirmer
Helga Schirmer*
Affiliation:
Carleton University, Ottawa, Canada
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 3 , June 1971 , pp. 461 - 467
Copyright
Copyright © Canadian Mathematical Society 1971

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